Download - Slope – Parallel and Perpendicular Lines
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