**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:

M

_{1}= (2- (-1))/(-1 - 5) = 3/(-6) = -1/2

M

_{2}= (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