holt ca course 1 8-5 coordinate geometry warm up warm up california standards california standards...
TRANSCRIPT
Holt CA Course 1
8-5 Coordinate Geometry
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
Holt CA Course 1
8-5 Coordinate Geometry
Warm UpComplete each sentence.
1. Two lines in a plane that never meet are called lines.
2. lines intersect at right angles.
3. The symbol || means that lines are .4. When a transversal intersects two lines, all of the acute angles are congruent.
parallel
Perpendicular
parallelparallel
Holt CA Course 1
8-5 Coordinate Geometry
MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.
Also covered: AF3.3
California
Standards
Holt CA Course 1
8-5 Coordinate Geometry
Vocabularypolygon
quadrilateral
trapezoid
parallelogram
rectangle
rhombus
square
Holt CA Course 1
8-5 Coordinate Geometry
In computer graphics, a coordinate system is used to create images, from simple geometric figures to realistic figures used in movies.
Properties of the coordinate plane can be used to find information about figures in the plane, such as whether lines in the plane are parallel.
Holt CA Course 1
8-5 Coordinate Geometry
Slopes of Parallel and Perpendicular Lines
• Any two nonvertical lines with equal slopes are parallel. Any two vertical lines are parallel.
• Any two nonvertical lines whose slope have a product of –1 are perpendicular. Vertical and horizontal lines are perpendicular.
Holt CA Course 1
8-5 Coordinate GeometryAdditional Example 1: Finding Perpendicular and Parallel
Lines Which lines are parallel? Which lines are perpendicular?
slope of EF = 32
slope of GH = 35
slope of PQ = 35
slope of QR = or –1 3 –3
2 3
slope of CD = or – –2 3
Step 1 Find the slope of each line.
Holt CA Course 1
8-5 Coordinate GeometryAdditional Example 1 Continued
The slopes are equal. =35
35
The slopes have a product
of –1: • – = –132
2 3
GH || PQ
EF CD
Which lines are parallel? Which lines are perpendicular?Step 2 Compare the slopes.
Holt CA Course 1
8-5 Coordinate GeometryCheck It Out! Example 1
A
C
B
D
F
E
K
JH
G
Which lines are parallel? Which lines are perpendicular?
slope of AB = or –6 4
–3 2
slope of CD = –2 3
slope of EF = or –4 6
–2 3
slope of GH = 23
slope of JK = or 1 3 3
Step 1 Find the slope of each line.
Holt CA Course 1
8-5 Coordinate Geometry
CD || EF
GH AB
A
C
B
D
F
E
K
JH
G
Check It Out! Example 1 Continued
Which lines are parallel? Which lines are perpendicular?
The slopes are equal. =–2 3
–2 3
The slopes have a product
of –1: • – = –123
3 2
Step 2 Compare the slopes.
Holt CA Course 1
8-5 Coordinate Geometry
A polygon is a closed plane figure formed by three or more line segments called sides. Each side meets exactly two other sides, one on each end, in a common endpoint. Quadrilaterals are polygons with four sides and four angles. Quadrilaterals with certain properties are given additional names.
Holt CA Course 1
8-5 Coordinate Geometry
Holt CA Course 1
8-5 Coordinate Geometry
Additional Example 2: Using Coordinates to Classify Quadrilaterals
Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral.
A(3, –2), B(2, –1), C(4, 3), D(5, 2)
parallelogram
CD || BA and BC || AD
Holt CA Course 1
8-5 Coordinate Geometry
R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
parallelogram, rectangle, rhombus, square
Check It Out! Example 2
Graph the quadrilateral with the given vertices. Give all the names that apply to the quadrilateral.
TU || SR and ST || RU
TURU, RURS, RSST and STTU
2 pairs of parallel sides, 4 right angles.
Holt CA Course 1
8-5 Coordinate Geometry
Rectangle WXYZ with W(–2, 2), X(3, 2), and Y(3, –4)
Step 2 Complete the figure to find the missing vertex.
Additional Example 3: Finding the Coordinates of a Missing Vertex
Find the coordinates of the missing vertex.
W
Y
X
Z
Step 1 Graph and connect the given points.
The coordinates of Z are (–2, –4).
Holt CA Course 1
8-5 Coordinate Geometry
Rectangle JKLM with J(– 1, 2), K(4, 2), and L(4, –1)
Step 2 Complete the figure to find the missing vertex.
Check It Out! Example 3
Find the coordinates of the missing vertex.
J
L
K
M
Step 1 Graph and connect the given points.
The coordinates of M are (–1, –1).
Holt CA Course 1
8-5 Coordinate Geometry
Lesson Quiz
Determine the slope of each line.
1. PQ
2. MN
3. MQ
4. NP
5. Which pair of lines are parallel?
1
8
7
– 10 3
MN, RQ