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8-5 Coordinate Geometry
Preview
Warm Up
California Standards
Lesson Presentation
Holt CA Course 1
8-5 Coordinate Geometry
Warm Up
Complete each sentence.
1. Two lines in a plane that never meet are called
parallel lines.
2. Perpendicular lines intersect at right angles.
3. The symbol || means that lines are parallel .
4. When a transversal intersects two parallel lines,
all of the acute angles are congruent.
Holt CA Course 1
8-5 Coordinate Geometry
California
Standards
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:
Holt CA Course 1
AF3.3
8-5 Coordinate Geometry
Vocabulary
polygon
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 Geometry
Additional Example 1: Finding Perpendicular and
Parallel Lines
Which lines are parallel? Which lines are
perpendicular?
Step 1 Find the slope of each line.
3
2
3
slope of GH =
5
3
slope of PQ =
5
–2
2
slope of CD =
or –
3
3
3
slope of QR =
or –1
–3
slope of EF =
Holt CA Course 1
8-5 Coordinate Geometry
Additional Example 1 Continued
Which lines are parallel? Which lines are
perpendicular?
Step 2 Compare the slopes.
GH || PQ
The slopes are equal.
3
3
=
5
5
EF  CD
The slopes have a product
2
3
of –1:
•–
= –1
3
2
Holt CA Course 1
8-5 Coordinate Geometry
Check It Out! Example 1
Which lines are parallel? Which lines are
perpendicular?
Step 1 Find the slope of each line.
–6
–3
or
4
2
–2
slope of CD =
3
–4
–2
slope of EF =
or
6
3
2
slope of GH =
3
3
slope of JK =
or 1
3
slope of AB =
Holt CA Course 1
A
C
K
D
E
H
J
B
G
F
8-5 Coordinate Geometry
Check It Out! Example 1 Continued
Which lines are parallel? Which lines are
perpendicular?
Step 2 Compare the slopes.
CD || EF
A
–2 –2
The slopes are equal.
=
3
3
C
K
GH  AB
The slopes have a product
3
2
of –1:
•–
= –1
2
3
Holt CA Course 1
D
E
H
J
B
G
F
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)
CD || BA and BC || AD
parallelogram
Holt CA Course 1
8-5 Coordinate Geometry
Check It Out! Example 2
Graph the quadrilateral with the given vertices.
Give all the names that apply to the quadrilateral.
R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
TU || SR and ST || RU
TURU, RURS, RSST and
STTU
2 pairs of parallel sides, 4
right angles.
parallelogram, rectangle,
rhombus, square
Holt CA Course 1
8-5 Coordinate Geometry
Additional Example 3: Finding the Coordinates
of a Missing Vertex
Find the coordinates of the missing vertex.
Rectangle WXYZ with W(–2, 2), X(3, 2), and
Y(3, –4)
Step 1 Graph and connect
the given points.
W
X
Step 2 Complete the figure
to find the missing vertex.
The coordinates of Z are
(–2, –4).
Holt CA Course 1
Z
Y
8-5 Coordinate Geometry
Check It Out! Example 3
Find the coordinates of the missing vertex.
Rectangle JKLM with J(– 1, 2), K(4, 2), and
L(4, –1)
Step 1 Graph and connect
the given points.
Step 2 Complete the figure
to find the missing vertex.
The coordinates of M are
(–1, –1).
Holt CA Course 1
J
K
M
L
8-5 Coordinate Geometry
Lesson Quiz
Determine the slope of each line.
1. PQ 1
2. MN –
10
3
3. MQ 8
4. NP 7
5. Which pair of lines are parallel?
MN, RQ
Holt CA Course 1