4.3 Parallels and Perpendiculars

Warm-up (IN)

Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify properties of

perpendicular bisectors.

Find the slope of the line through each pair of points:

1. (-3,4) and (7,-1) 2. (6,-2) and (9,4)

Give the slope and y-int for each line:

3. y=-3x+6 4. y=5(x-2)

5. Write an equation for the line through (5,-2) with slope -3.

-1/2

2

m=-3, b=6

m=5, b=-10

y=-3x+13

Notes

Parallel Lines -

Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify properties of perpendicular bisectors.

Slopes are the same

Perpendicular Lines - Slopes are opposite reciprocals

Their product is -1

Ex 1 – In Quad GLAD, is the bisector of ?GA LD

Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify properties of perpendicular bisectors.

G(0,5) L(5,6)

A(8,1) D(3,0)

mdpt LD

,

2 2

5 3 6 0 4,3

mdpt GA

,

2 2

0 8 5 1 4,3

Bisect each other! ?slopeLD

6-0

5 -3=

6

2=3 slopeGA

5-1

0 -8=

4

-8=-1/2

NO!!

Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify properties of perpendicular bisectors.

Ex 2 – Write an equation of the line that goes through the point (-2,1) and is parallel to 2

23

y x

2

3m y mx b

1 2

3 2 b

14

3 b

7

3b

y 2

3x

7

3

Learning Objective: to find the slopes and write equations of parallel and perpendicular lines and to identify properties of perpendicular bisectors.

Ex 3 – Write an equation of the line that goes through the point (-2,1) and is to 2

23

y x

3

2m y mx b

1 2 b

1 3 b

2 b

y x 2

3

2

3

2

HW – p. 183-185 #1-3, 4-22 even, 28-31

Out – Explain how you could use slopes to show that a triangle is right.

Summary – I’m glad I remember _______ or I wish I remembered ______ about lines.

POW!!