You will learn to name and graph ordered

pairs on acoordinate plane.

In coordinate geometry, grid paper is used to

locate points.

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

You will learn to find the distance of a line

segment.

The distance of a line segment AB is found by the formula

BA

d (x2 x1)2 (y2 y1)

2

You will learn to find the coordinates of the

midpoint of a segment.

bisectsThe midpoint of a line segment AB

is the point C that ______ the segment.

BA C

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

The horizontal number lineis called the ______.x-axis

The vertical number lineis called the ______.y-axis

O

Quadrant I(+, +)

Quadrant II

(–, +)

Quadrant III

(–, –)

Quadrant IV

(+, –)

Lets’ lookat thegrid.

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

O

The point of intersection of the twoaxes is called the _____.origin

The two axes separate the plane intofour regions called _________.quadrants

Quadrant I(+, +)

Quadrant II

(–, +)

Quadrant III

(–, –)

Quadrant IV

(+, –)

Lets’ lookat thegrid.

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

Point A(x, y) =

Point B(x, y) =

Point C(x, y) =

Point D(x, y) =

A

(3, 2)

(–3, 2) B

(–3, –2)C (3, –2)D

(3, 2)A

DC

B

(–3, –2)

(–3, 2) (3, –2)

Now, see if you can name the

points.

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

A(2, 4)B(2, 0)C(2, –3)D(2, –5)

On a piece of grid paper draw lines

representing the x-axis and the y-axis.

Graph :

OK, It’s your turn

A

B

C

D

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

Consider these questions:

What do you notice about the graphs of

these points?

They lie on a vertical

line.

OK, It’s your turn

A

B

C

D

x = 2

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

Consider these questions:

What do you notice about the x-coordinates

of these points?

They are the same

number.

OK, It’s your turn

A

B

C

D

A(2, 4)B(2, 0)C(2, –3)D(2, –5)

y

x5-4 -2 1 3 5

5

-4

-2

1

3

5

-5 -1 4

-5

-1

4

-3

-5

2

2-5

-3

Consider these questions:

Write a general statement about ordered pairs that

have the same x-coordinate.

They lie on a vertical line

that intersects the x-axis at

the x-coordinate.

OK, It’s your turn

A

B

C

D

d (x2 x1)2 (y2 y1)

2

Find the distance between two points.

(-2,5) and (8,3)

d (8 2)2 (3 5)2

d=10.19803903

How about thedistance between

two points

Find the midpoint between two

points.

(0.45,7) and (-0.3,-9)

(0.075,-1)

x2 x1

2,y2 y1

2

0.3 0.45

2, 9 7

2

Lets’ look at finding a midpoint.

0

y

0 x

10-1 2 4 6 8 10

10

-1

2

4

6

8

10

-2 3 7-2

1

5

9

1 9

3

-2-2

5

7

Find the midpoint, C(x, y), of a segment on the coordinate plane.

x = 1 x = 9

y = 7

y = 3

A(1, 7)

B(9, 3)

x

yC(5, 5)

0

y

0 x

10-1 2 4 6 8 10

10

-1

2

4

6

8

10

-2 3 7-2

1

5

9

1 9

3

-2-2

5

7

Graph A(1, 1) and B(7, 9)

C

Draw AB

B(7, 9)

A(1, 1)

Find the midpointof AB.

C(4, 5)

x-coordinate of B y-coordinate of B

Replace x1 with 7and y1 with 2

Multiply each side by 2

Add or subtract toisolate the variable

A(7, 2)

B(x, y) is somewhere over there.

B(-1, 8)

midpoint

C(3, 5)

Suppose C(3, 5) is the midpointof AB. Find the coordinate of B.

5x - 6 2x

CBA

Since B is the midpoint: AB = BC

Write the equation involving x: 5x – 6 = 2x

Solve for x: 5x – 2x – 6 = 2x – 2x

3x – 6 + 6 = 0 + 6

3x = 6

x = 2

AB = 5x – 6 = 5(2) – 6 = 10 – 6 = 4

BC = 2x = 2(2) = 4

Check!

In the figure, B is the midpoint of AC.

Find the value of x.

6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?

7. In the figure below, R is the midpoint of QS. Find the value of d.

8. True or False: If AB CD, then CD AB.

9. True or False: If AB BC, then B is the midpoint of AC.

1.8 The Coordinate PlanGeometry

1. Name the coordinates of each point.

2. Graph point C at (0, –4).

4. Graph y = 2.

3. Graph x = –4.

5. Graph and label the intersection of x = –4 and y = 2

0

y

x

5-1 2 4

4

0

-2 1-3

2

3-2

-2

A

B

10. Find the distance: (-4,9),(1,-3)

11. Find the midpoint: (9,-2),(12,-14)

d + 4 3d

SRQ

6. DF is bisected at point E, and DF = 8. What do you know about the lengths of DE and EF ?

7. In the figure below, R is the midpoint of QS. Find the value of d.

8. True or False: If AB CD, then CD AB.

9. True or False: If AB BC, then B is the midpoint of AC.

1.8 The Coordinate PlanGeometry

1. Name the coordinates of each point.

A = (2, 0)

B = (3, –2)

2. Graph point C at (0, –4).

4. Graph y = 2.

3. Graph x = –4.

5. Graph and label the intersection of x = –4 and y = 2

0

y

x

5-1 2 4

4

0

-2 1-3

2

3-2

-2

A

B

10. Find the distance: (-4,9),(1,-3)

11. Find the midpoint: (9,-2),(12,-14)

d + 4 3d

SRQ