Slope – Parallel and Perpendicular Lines

Mrs. King and Mr. ZampettiGeometryUnit 12, Day 9

http://jwelker.lps.org/lessons/ppt/geod_3_3_slope.ppt

Slope - Defined

Given two points (x1, y1) and (x2, y2), the slope m of a line is defined to be:

2 1

2 1

y y yorx x x

m

Slope – Example #1

Given two points A(-3, -4) and B(3, 5), find the slope of the line through the points.

2 1

2 1

y y yorx x x

m

Solution:

5 ( 4)3 ( 3)

m

5 4 93 3 6

Reduce fractions whenever possible.

32

m

Slope – Example #2a2 1

2 1

y y yorx x x

m

Find the slope of the line AB.

A(-4, 4) B(1, 7)

7 4 31 ( 4) 5

m

The slope of the line through AB is 3/5.

Slope – Example #2c2 1

2 1

y y yorx x x

m

On your own:

Find the slope of EF.

The slope of EF is -2/3.

Since the slope is negative, the line runs down as we look from left to right. Positive slope runs up from left to right.

Slope – Example #2d2 1

2 1

y y yorx x x

m

On your own:

Find the slope of CF.

C(3,7) F(3, -6)

6 7 133 3 0

m

Since division by zero is not defined, the slope of CF is undefined.

Slope – Vertical Lines2 1

2 1

y y yorx x x

m

The slope of any vertical line is undefined.

Slope – Example #32 1

2 1

y y yorx x x

m

On your own:

Find the slope of MN.

M(-1, 2) N(3, 2)

2 2 03 ( 1) 4

m

The slope of MN is 0. MN is said to have zero slope.

Slope – Horizontal Lines2 1

2 1

y y yorx x x

m

The slope of any horizontal line is zero.

Slope – Other Lines 2 1

2 1

y y yorx x x

m

Find the slope of PQ, RS, and TU.

13133

m of PQ

m of RS

m of TU

What can be said about lines PQ and RS?

The lines are parallel and have the same slope.

Slope – Parallel Lines2 1

2 1

y y yorx x x

m

Parallel lines have equal slopes.

Slope – Other Lines 2 1

2 1

y y yorx x x

m

13133

m of PQ

m of RS

m of TU

What can be said about lines PQ and TU?

The lines are perpendicular and have slopes which multiply to -1.

Slope – Perpendicular Lines2 1

2 1

y y yorx x x

m

Perpendicular lines have slopes which:

• multiply to -1

• are negative reciprocals of each other.

Horizontal and vertical lines are perpendicular to each other.

Slope – Example #42 1

2 1

y y yorx x x

m

Points R(3, -2) and S(-1, 3) form a line.

a) find the slope of RS.

3 ( 2) 5 541 3 4

m

b) find the slope of a line perpendicular to RS.

Since perpendicular lines have slopes which are negative reciprocals, the slope of the perpendicular line is 4/5.

Practice

Matching Game: Calculate the slope!http://www.quia.com/mc/499415.html

Homework

Work Packet: Slope, Parallel and Perpendicular Lines