7-5
Coordinate Geometry
Warm Up
Problem of the Day
Lesson Presentation
Course 3
7-5 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.
Course 3
7-5 Coordinate Geometry
Problem of the Day
What type of polygon am I? My opposite
angles have equal measure. I do not have a
right angle. All my sides are congruent.
rhombus
Course 3
7-5 Coordinate Geometry
Learn to identify polygons in the
coordinate plane.
Course 3
Coordinate
Geometry
7-5 Insert
Lesson
Title Here
Vocabulary
slope
rise
run
Course 3
7-5 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.
Course 3
7-5 Coordinate Geometry
Slope is a number that describes how steep a
line is.
rise
vertical change
slope =
=
run
horizontal change
Course 3
7-5 Coordinate Geometry
The slope of a horizontal line is 0. The
slope of a vertical line is undefined.
Remember!
When a nonzero number is divided by zero,
the quotient is undefined. There is no
answer.
Course 3
7-5 Coordinate Geometry
Additional Example 1A: Finding the Slope of a Line
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
XY
positive slope;
–5
slope of XY = –4 =
Course 3
5
4
7-5 Coordinate Geometry
Additional Example 1B: Finding the Slope of a Line
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
ZA
negative slope;
1
slope of ZA = –1 = –
2
2
Course 3
7-5 Coordinate Geometry
Additional Example 1C: Finding the Slope of a Line
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
BC
slope of BC is undefined
Course 3
7-5 Coordinate Geometry
Additional Example 1D: Finding the Slope of a Line
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
DM
slope of DM = 0
Course 3
7-5 Coordinate Geometry
Check It Out: Example 1A
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
B
A
AB
C
positive slope;
slope of AB =
1
8
F
G
D
Course 3
E
H
7-5 Coordinate Geometry
Check It Out: Example 1B
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
B
A
CD
slope of CD is undefined
C
E
F
G
D
Course 3
H
7-5 Coordinate Geometry
Check It Out: Example 1C
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
B
A
EF
slope of EF = 0
C
E
F
G
D
Course 3
H
7-5 Coordinate Geometry
Check It Out: Example 1D
Determine if the slope of each line is positive,
negative, 0, or undefined. Then find the slope
of each line.
B
A
GH
negative slope;
1
slope of GH = –1 = –
3
3
C
F
G
D
Course 3
E
H
7-5 Coordinate Geometry
Slopes of Parallel and Perpendicular Lines
Two lines with equal slopes are parallel.
Two lines whose slopes have a product of –1
are perpendicular.
Helpful Hint
If a line has slope a , then a line
b
b
perpendicular to it has slope – a .
Course 3
7-5 Coordinate Geometry
Additional Example 2: Finding Perpendicular
Line and Parallel Lines
Which lines are parallel? Which lines are
perpendicular?
3
slope of EF =
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
Course 3
7-5 Coordinate Geometry
Additional Example 2 Continued
Which lines are parallel? Which lines are
perpendicular?
GH || PQ
3
3
The slopes are equal.
=
5
5
EF  CD
The slopes have a product
2
3
of –1:
•–
= –1
3
2
Course 3
7-5 Coordinate Geometry
Check It Out: Example 2
Which lines are parallel? Which lines are
perpendicular?
–6
–3
slope of AB =
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
Course 3
A
C
K
D
E
H
J
B
G
F
7-5 Coordinate Geometry
Check It Out: Example 2 Continued
Which lines are parallel? Which lines are
perpendicular?
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
Course 3
D
E
H
J
B
G
F
7-5 Coordinate Geometry
Additional Example 3A: Using Coordinates to
Classify Quadrilaterals
Graph the quadrilaterals with the given vertices.
Give all the names that apply to each quadrilateral.
A(3, –2), B(2, –1), C(4, 3), D(5, 2)
CD || BA and BC || AD
parallelogram
Course 3
7-5 Coordinate Geometry
Additional Example 3B: Using Coordinates to
Classify Quadrilaterals
Graph the quadrilaterals with the given vertices.
Give all the names that apply to each 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
parallelogram, rectangle,
rhombus, square
Course 3
7-5 Coordinate Geometry
Check It Out: Example 3A
Graph the quadrilaterals with the given vertices.
Give all the names that apply to each
quadrilateral.
A(–1, 3), B(1, 5), C(7, 5), D(5, 3)
B
CD || BA and BC || AD
A
parallelogram
Course 3
C
D
7-5 Coordinate Geometry
Check It Out: Example 3B
Graph the quadrilaterals with the given vertices.
Give all the names that apply to each
quadrilateral.
E(1, 5), F(7, 5), G(6, 1), H(2, 1)
EF || HG
E
F
trapezoid
H
Course 3
G
7-5 Coordinate Geometry
Additional Example 4: 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).
Course 3
Z
Y
7-5 Coordinate Geometry
Additional Example 4B: Finding the Coordinates
of a Missing Vertex
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).
Course 3
J
K
M
L
Coordinate
Geometry
7-5 Insert
Lesson
Title Here
Lesson Quiz
Determine the slope of each line.
1. PQ 1
10
2. MN –
3
3. MQ 8
4. NP 7
5. Which pair of lines are parallel?
MN, RQ
Course 3