56 the rectangular coordinate system
TRANSCRIPT
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Rectangular Coordinate System
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A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D).
Rectangular Coordinate System
![Page 3: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/3.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
![Page 4: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/4.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
![Page 5: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/5.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis.
![Page 6: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/6.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis. The vertical axis is called the y-axis.
![Page 7: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/7.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.
![Page 8: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/8.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.Starting from the origin, each point is addressed by its ordered pair (x, y) where:
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A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.Starting from the origin, each point is addressed by its ordered pair (x, y) where:x = amount to move right (+) or left (–).
![Page 10: 56 the rectangular coordinate system](https://reader036.vdocuments.net/reader036/viewer/2022062503/587e54fb1a28abeb1a8b69e5/html5/thumbnails/10.jpg)
A coordinate system is a system of assigning addresses for positions in the plane (2 D) or in space (3 D). The rectangular coordinate system for the plane consists of a rectangular grid where each point in the plane is addressed by an ordered pair of numbers (x, y).
Rectangular Coordinate System
The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the axes meet is called the origin.Starting from the origin, each point is addressed by its ordered pair (x, y) where:x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).
Rectangular Coordinate System
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3)
Rectangular Coordinate System
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right,
Rectangular Coordinate System
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
(4, –3)P
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
A
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
A
B
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
A
B
C
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate.
A
B
C
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate.
A
B
C
Example B: Find the coordinate of P, Q, R as shown.
P
Q
R
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate.
A
B
C
Example B: Find the coordinate of P, Q, R as shown.P(4, 5),
P
Q
R
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate.
A
B
C
Example B: Find the coordinate of P, Q, R as shown.P(4, 5), Q(3, -5),
P
Q
R
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x = amount to move right (+) or left (–). y = amount to moveup (+) or down (–).For example, the point P corresponds to (4, –3) is4 right, and 3 down from the origin.
Rectangular Coordinate System
Example A. Label the points A(-1, 2), B(-3, -2),C(0, -5).
The ordered pair (x, y) corresponds to a point is called the coordinate of the point, x is the x-coordinate and y is the y-coordinate.
A
B
C
Example B: Find the coordinate of P, Q, R as shown.P(4, 5), Q(3, -5), R(-6, 0)
P
Q
R
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The coordinate of the origin is (0, 0).
(0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(5, 0) (0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(5, 0)(-6, 0) (0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(5, 0)(-6, 0)
Any point on the y-axishas coordinate of the form (0, y). (0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(5, 0)(-6, 0)
Any point on the y-axishas coordinate of the form (0, y).
(0, 6)
(0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).
(5, 0)(-6, 0)
Any point on the y-axishas coordinate of the form (0, y).
(0, -4)
(0, 6)
(0,0)
Rectangular Coordinate System
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).Any point on the y-axishas coordinate of the form (0, y).
Rectangular Coordinate System
The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV.
QIQII
QIII QIV
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).Any point on the y-axishas coordinate of the form (0, y).
Rectangular Coordinate System
The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV.
QIQII
QIII QIV
(+,+)
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).Any point on the y-axishas coordinate of the form (0, y).
Rectangular Coordinate System
The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV.
QIQII
QIII QIV
(+,+)(–,+)
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The coordinate of the origin is (0, 0).Any point on the x-axishas coordinate of the form (x, 0).Any point on the y-axishas coordinate of the form (0, y).
Rectangular Coordinate System
(+,+)(–,+)
(–,–) (+,–)
The axes divide the plane into four parts. Counter clockwise, they are denoted as quadrants I, II, III, and IV. Respectively, the signs of the coordinates of each quadrant are shown.
QIQII
QIII QIV
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.
(5,4)
Rectangular Coordinate System
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.
(5,4)(–5,4)
Rectangular Coordinate System
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis.
(5,4)(–5,4)
Rectangular Coordinate System
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis.
(5,4)(–5,4)
(5, –4)
Rectangular Coordinate System
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis.
(5,4)(–5,4)
(5, –4) (–x, –y) is the reflection of (x, y) across the origin.
Rectangular Coordinate System
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When the x-coordinate of the a point (x, y) is changed to its opposite as (–x , y), the new point is the reflectionacross the y-axis.When the y-coordinate of the a point (x, y) is changed to its opposite as (x , –y), the new point is the reflection across the x-axis.
(5,4)(–5,4)
(5, –4) (–x, –y) is the reflection of (x, y) across the origin.
(–5, –4)
Rectangular Coordinate System
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Movements and CoordinatesRectangular Coordinate System
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Movements and CoordinatesLet A be the point (2, 3).
Rectangular Coordinate System
A(2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3)
Rectangular Coordinate System
A(2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B,
Rectangular Coordinate System
A B(2, 3) (6, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
x–coord. increased by 4
(2, 3) (6, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3)
x–coord. increased by 4
(2, 3) (6, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C,
C
x–coord. increased by 4
x–coord. decreased by 4
(2, 3) (6, 3)(–2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4.
C
x–coord. increased by 4
x–coord. decreased by 4
(2, 3) (6, 3)(–2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4.
Hence we conclude that changes in the x–coordinates of a point move the point right and left.
C
x–coord. increased by 4
x–coord. decreased by 4
(2, 3) (6, 3)(–2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4.
Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right.
C
x–coord. increased by 4
x–coord. decreased by 4
(2, 3) (6, 3)(–2, 3)
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Movements and CoordinatesLet A be the point (2, 3). Suppose it’s x–coordinate is increased by 4 to (2 + 4, 3) = (6, 3) - to the point B, this corresponds to moving A to the right by 4.
Rectangular Coordinate System
A B
Similarly if the x–coordinate of (2, 3) is decreased by 4 to (2 – 4, 3) = (–2, 3) - to the point C, this corresponds to moving A to the left by 4.
Hence we conclude that changes in the x–coordinates of a point move the point right and left. If the x–change is +, the point moves to the right. If the x–change is – , the point moves to the left.
C
x–coord. increased by 4
x–coord. decreased by 4
(2, 3) (6, 3)(–2, 3)
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Again let A be the point (2, 3).
Rectangular Coordinate System
A(2, 3)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7)
Rectangular Coordinate System
A(2, 3)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D,
Rectangular Coordinate System
A
Dy–coord. increased by 4
(2, 3)
(2, 7)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
Dy–coord. increased by 4
(2, 3)
(2, 7)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
D
Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E,
E
y–coord. increased by 4
y–coord. decreased by 4
(2, 3)
(2, 7)
(2, –1)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
D
Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4.
E
y–coord. increased by 4
y–coord. decreased by 4
(2, 3)
(2, 7)
(2, –1)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
D
Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4.
Hence we conclude that changes in the y–coordinates of a point move the point right and left.
E
y–coord. increased by 4
y–coord. decreased by 4
(2, 3)
(2, 7)
(2, –1)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
D
Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4.
Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up.
E
y–coord. increased by 4
y–coord. decreased by 4
(2, 3)
(2, 7)
(2, –1)
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Again let A be the point (2, 3). Suppose its y–coordinate is increased by 4 to (2, 3 + 4) = (2, 7) - to the point D, this corresponds to moving A up by 4.
Rectangular Coordinate System
A
D
Similarly if the y–coordinate of (2, 3) is decreased by 4 to (2, 3 – 4) = (2, –1) - to the point E, this corresponds to moving A down by 4.
Hence we conclude that changes in the y–coordinates of a point move the point right and left. If the y–change is +, the point moves up.If the y–change is – , the point moves down.
E
y–coord. increased by 4
y–coord. decreased by 4
(2, 3)
(2, 7)
(2, –1)
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4)
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4).
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100)
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104).
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
We need to add 50 to the x–coordinate (to the right)
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down).
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30)
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30) = (48, –26).
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Rectangular Coordinate SystemExample. C.a. Let A be the point (–2, 4). What is the coordinate of the point B that is 100 units directly left of A?
Moving left corresponds to decreasing the x-coordinate.Hence B is (–2 – 100, 4) = (–102, 4). b. What is the coordinate of the point C that is 100 units directly above A?
Moving up corresponds to increasing the y-coordinate.Hence C is (–2, 4) = (–2, 4 +100) = (–2, 104). c. What is the coordinate of the point D that is 50 to the right and 30 below A?
We need to add 50 to the x–coordinate (to the right) and subtract 30 from the y–coordinate (to go down). Hence D has coordinate (–2 + 50, 4 – 30) = (48, –26).
Coordinate systems are used beside the geometric context
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Rectangular Coordinate SystemMeasurements often are recorded as two related numbers.
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Rectangular Coordinate SystemMeasurements often are recorded as two related numbers. In example C. we plotted the following recorded temperatures 35o, 27o, –40o, –25o, 16o, 21o at some location on a line.
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Rectangular Coordinate SystemMeasurements often are recorded as two related numbers. In example C. we plotted the following recorded temperatures 35o, 27o, –40o, –25o, 16o, 21o at some location on a line.
time (pm) temperature
1 35
2 27
3 –40
4 –25
5 16
6 21
Suppose these numbers were recorded at different times shown on the table below, then we can plot the data using the rectangular coordinate systems.
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Rectangular Coordinate System
Example. D. a. Plot the table using the time and temperature axes.
Measurements often are recorded as two related numbers. In example C. we plotted the following recorded temperatures 35o, 27o, –40o, –25o, 16o, 21o at some location on a line.
time (pm) temperature
1 35
2 27
3 –40
4 –25
5 16
6 21
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
Suppose these numbers were recorded at different times shown on the table below, then we can plot the data using the rectangular coordinate systems.
pm
temp.
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Rectangular Coordinate System
Example. D. a. Plot the table using the time and temperature axes.
Measurements often are recorded as two related numbers. In example C. we plotted the following recorded temperatures 35o, 27o, –40o, –25o, 16o, 21o at some location on a line.
time (pm) temperature
1 35
2 27
3 –40
4 –25
5 16
6 21
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
Suppose these numbers were recorded at different times shown on the table below, then we can plot the data using the rectangular coordinate systems.
pm
temp.
(1, 35)
(2, 27)
(3, –40)
(4, –25)
(5, 15)(6, 21)
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Rectangular Coordinate System
Example. D. a. Plot the table using the time and temperature axes.
Measurements often are recorded as two related numbers. In example C. we plotted the following recorded temperatures 35o, 27o, –40o, –25o, 16o, 21o at some location on a line.
time (pm) temperature
1 35
2 27
3 –40
4 –25
5 16
6 21
0o
40o
–40o
20o
–20o
10o
30o
–10o
–30o
Suppose these numbers were recorded at different times shown on the table below, then we can plot the data using the rectangular coordinate systems.
pm
temp.
(1, 35)
(2, 27)
(3, –40)
(4, –25)
(5, 15)(6, 21)
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Exercise. A.a. Write down the coordinates of the following points.
Rectangular Coordinate System
AB
C
D
EF
GH
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Ex. B. Plot the following points on the graph paper.Rectangular Coordinate System
2. a. (2, 0) b. (–2, 0) c. (5, 0) d. (–8, 0) e. (–10, 0)All these points are on which axis? 3. a. (0, 2) b. (0, –2) c. (0, 5) d. (0, –6) e. (0, 7)All these points are on which quadrant? 4. a. (5, 2) b. (2, 5) c. (1, 7) d. (7, 1) e. (6, 6)All these points are in which quadrant? 5. a. (–5, –2) b. (–2, –5) c. (–1, –7) d. (–7, –1) e. (–6, –6)All these points are in which quadrant? 6. List three coordinates whose locations are in the 2nd quadrant and plot them.7. List three coordinates whose locations are in the 4th quadrant and plot them.
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C. Find the coordinates of the following points. Draw both points for each problem.
Rectangular Coordinate System
The point that’s8. 5 units to the right of (3, –2).
10. 4 units to the left of (–1, –5). 9. 6 units to the right of (–4, 2).
11. 6 units to the left of (2, –6). 12. 3 units to the left and 6 units down from (–2, 5). 13. 1 unit to the right and 5 units up from (–3, 1). 14. 3 units to the right and 3 units down from (–3, 4). 15. 2 units to the left and 6 units up from (4, –1).
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Rectangular Coordinate SystemD. Given the following graph, answer the following questions.
16. What’s the temperaturechange from 1 pm to 2 pm?17. What’s the temperaturechange from 3 pm to 4 pm?18. Between what one hour period the temperature had risen the most?19. Between what one hour period the temperature had fallen the most?
20. What is the largest temperature difference through out the afternoon?
63