1. 7-5 Coordinate Geometry Warm Up Problem of the Day Lesson Presentation
Course 3

2. 7-5 Coordinate Geometry Warm Up Complete each sentence.
Course 3
7-5
Coordinate Geometry
Warm Up
Complete 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
parallel

3. 7-5 Coordinate Geometry Problem of the Day
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

4. 7-5 Learn to identify polygons in the coordinate plane.
Course 3
7-5
Coordinate Geometry
Learn to identify polygons in the coordinate plane.

5. Insert Lesson Title Here
Course 3
7-5
Coordinate Geometry
Insert Lesson Title Here
Vocabulary
slope
rise
run

6. 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.

7. vertical change horizontal change
Course 3
7-5
Coordinate Geometry
Slope is a number that describes how steep a line is.
vertical change horizontal change
rise run
slope = =

8. 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!

9. Additional Example 1A: Finding the Slope of a Line
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 5 4

10. Additional Example 1B: Finding the Slope of a Line
Course 3
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;
slope of ZA = = – –1 2 1

11. Additional Example 1C: Finding the Slope of a Line
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

12. Additional Example 1D: Finding the Slope of a Line
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

13. 7-5 Coordinate Geometry Check It Out: Example 1A
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
positive slope;
slope of AB = 1 8 C E F G H D

14. 7-5 Coordinate Geometry Check It Out: Example 1B
Course 3
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 H D

15. 7-5 Coordinate Geometry Check It Out: Example 1C
Course 3
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 H D

16. 7-5 Coordinate Geometry Check It Out: Example 1D
Course 3
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;
slope of GH = = – –1 3 1 C E F G H D

17. 7-5 Coordinate Geometry Slopes of Parallel and Perpendicular Lines
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

18. Additional Example 2: Finding Perpendicular Line and Parallel Lines
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 = 3 2
slope of GH = 3 5
slope of PQ = 3 5 2 3
slope of CD = or – –2
slope of QR = or –1 3 –3

19. Additional Example 2 Continued
Course 3
7-5
Coordinate Geometry
Additional Example 2 Continued
Which lines are parallel? Which lines are perpendicular?
GH || PQ
The slopes are equal. = 3 5
EF  CD
The slopes have a product
of –1: • – = –1 3 2

20. 7-5 Coordinate Geometry Check It Out: Example 2
Course 3
7-5
Coordinate Geometry
Check It Out: Example 2
Which lines are parallel? Which lines are perpendicular?
slope of AB = or –6 4 –3 2
slope of CD = –2 3 A
slope of EF = or –4 6 –2 3 C K D E
slope of GH = 2 3 H J B
slope of JK = or 1 3 G F

21. Check It Out: Example 2 Continued
Course 3
7-5
Coordinate Geometry
Check It Out: Example 2 Continued
Which lines are parallel? Which lines are perpendicular?
CD || EF
The slopes are equal. = –2 3 A C K D
GH  AB E H
The slopes have a product
of –1: • – = –1 2 3 J B G F

22. Additional Example 3A: Using Coordinates to Classify Quadrilaterals
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)
CD || BA and BC || AD
parallelogram

23. Additional Example 3B: Using Coordinates to Classify Quadrilaterals
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

24. 7-5 Coordinate Geometry parallelogram Check It Out: Example 3A
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 C A D
parallelogram

25. 7-5 Coordinate Geometry trapezoid Check It Out: Example 3B
Course 3
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 G

26. Additional Example 4: Finding the Coordinates of a Missing Vertex
Course 3
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). Y Z

27. Additional Example 4B: Finding the Coordinates of a Missing Vertex
Course 3
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. J K
Step 2 Complete the figure to find the missing vertex. L M
The coordinates of M are (–1, –1).

28. Insert Lesson Title Here
Course 3
7-5
Coordinate Geometry
Insert Lesson Title Here
Lesson Quiz
Determine the slope of each line.
1. PQ
2. MN
3. MQ
4. NP
5. Which pair of lines are parallel? 1 – 10 3 8 7
MN, RQ