Question

Given the ordered pairs A (-6, 4) and B(8, 9). Show all work!

a. Find the equation of the line through AB.
b. Find the equation of the line parallel to line AB and passes through the point (14, -6).
c. Find the equation of the line perpendicular to line AB and passes through the point (-5, -10).

Answer 1

Explanation:

Two points A and B are given

Using two point formula for straight lines we get

`(x+6)/(8+6) =(y-4)/(9-4) \\5(x+6) = 14(y-4)\\5x+30 = 14y-56\\5x-14y+86 =0`

b) A line parallel to AB would be of the form

5x-14y +k=0

Since the line passes through (14,-6) substitute to get k

5(14)-14(-6)+k=0 Or k = -154

Line is 5x-14y-154 =0

c) A line perpendicular to AB would have form as

14x+5y =k1

Substitute (-5,-10) to get k

14(-5)+5(-10) =k1

Or k1 = -120

Hence equation is 14x+5y = -120