Geometry chapter 3.7 Perpendicular lines in the Coordinate Plane:
I) Postulate:
A) In a coordinate plane, 2 non-vertical lines are perpendicular if and only if they product of their slopes is equal to (-1). The two slopes are negative reciprocals of each other.
all vertical and horizontal lines are perpendicular to each other.
Given the slope of the first line is a/b,
then the slope of the perpendicular line is (-b/a).
(a/b)(-b/a) = (-1)
B) To show that two lines are perpendicular lines:
1) Find the slopes of each line
2) multiply the slopes
3) Perpendicular if they = -1
Example: Given the first line has points (-1,2) and (5, -1) and the second line has points (4,2) and (1, -4), find out if the two lines are perpendicular:
M1 = (2- (-1))/(-1 - 5) = 3/(-6) = -1/2
M2 = (2 - (-4))/(4 - 1) = 6/3 = 2
when you multiply these together (-1/2)(2) = -1
so these lines are perpendicular to each other.
Example 2:
Given the slope of the first line is 3/4, what is the slope of a line perpendicular to this line and what is the equation of the line perpendicular through the point (9, -2)
y = mx + b
the slope was 3/4 so the perpendicular slope is (-4/3)
-2 = (-4/3)(9) + b
-2 = -12 + b
10 = b
therefore the equation of the line perpendicular to the first line through the point (6, -2) is
y = (-4/3) x + 10
