Question

Given U(-4,-1) and V(7,1), write an equation for the line through U and Perpendicular to UV

Answer 1

`y = -(11)/(2)x - 23`

Explanation:

Perpendicular lines are lines which intersect at a 90 degree angle. They also are lines which slopes are negative reciprocals of each other. The line UV has slope 2/11. This is found using the slope formula:

`m = (y_2-y_1)/(x_2-x_1) = (1--1)/(7--4)= (2)/(11)`

Since it will be perpendicular the slope is -11/2. Substitute m = -11/2 and the point (-4,-1) into the point slope form.

`y - y_1 = m(x-x_1)\\y - -1 = -(11)/(2)(x - -4)\\y +1 = -(11)/(2)(x + 4)\\y + 1 = -(11)/(2)x - 22\\y = -(11)/(2)x - 23`