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7-5 Coordinate Geometry
Course 3
Warm Up
Problem of the Day
Lesson Presentation
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
parallel
Course 3
7-5 Coordinate Geometry
parallel
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
7-5 Coordinate Geometry
Vocabularyslope
rise
run
Insert Lesson Title Here
Course 3
7-5 Coordinate Geometry
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.
slope =vertical change
horizontal changerise run=
Course 3
7-5 Coordinate Geometry
The slope of a horizontal line is 0. The slope of a vertical line is undefined.
When a nonzero number is divided by zero, the quotient is undefined. There is no answer.
Remember!
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;
slope of XY = = –5–4
54
Course 3
7-5 Coordinate Geometry
Determine if the slope of each line is positive, negative, 0, or undefined. Then find the slope of each line.
ZA
negative slope;
slope of ZA = = ––1 2
12
Additional Example 1B: Finding the Slope of a Line
Course 3
7-5 Coordinate Geometry
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
Additional Example 1C: Finding the Slope of a Line
Course 3
7-5 Coordinate Geometry
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
Additional Example 1D: Finding the Slope of a Line
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.
AB A
C
B
D
FE
HG
positive slope;
slope of AB = 1 8
Course 3
7-5 Coordinate Geometry
CD
slope of CD is undefined
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.
A
C
B
D
FE
HG
Course 3
7-5 Coordinate Geometry
EF
slope of EF = 0
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.
A
C
B
D
FE
HG
Course 3
7-5 Coordinate Geometry
GH
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.
A
C
B
D
FE
HG
negative slope;
slope of GH = = ––1 3
13
Course 3
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.
If a line has slope , then a line
perpendicular to it has slope – .
Helpful Hint a b b
a
Course 3
7-5 Coordinate Geometry
Additional Example 2: Finding Perpendicular Line 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
Course 3
7-5 Coordinate Geometry
Additional Example 2 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?
Course 3
7-5 Coordinate Geometry
Check It Out: Example 2
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
Course 3
7-5 Coordinate Geometry
CD || EF
GH AB
A
C
B
D
F
E
K
JH
G
Check It Out: Example 2 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
Course 3
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)
parallelogram
CD || BA and BC || AD
Course 3
7-5 Coordinate Geometry
R(–3, 1), S(–4, 2), T(–3, 3), U(–2, 2)
parallelogram, rectangle, rhombus, square
Additional Example 3B: Using Coordinates to Classify Quadrilaterals
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
TU || SR and ST || RU
TURU, RURS, RSST and STTU
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)
parallelogram
A
CB
D
CD || BA and BC || AD
Course 3
7-5 Coordinate Geometry
E(1, 5), F(7, 5), G(6, 1), H(2, 1)
trapezoid
E F
H G
EF || HG
Check It Out: Example 3B
Graph the quadrilaterals with the given vertices. Give all the names that apply to each quadrilateral.
Course 3
7-5 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 4: 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).
Course 3
7-5 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.
Additional Example 4B: Finding the Coordinates of a Missing Vertex
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).
Lesson Quiz
Determine the slope of each line.
1. PQ
2. MN
3. MQ
4. NP
5. Which pair of lines are parallel?
1
Insert Lesson Title Here
8
7
Course 3
7-5 Coordinate Geometry
– 10 3
MN, RQ