Find the value of x so the line that passes through (x, 2) and (-4, 5) is perpendicular to the line that passes through (4,8) and (2,-1)

x = 19/2

Step-by-step explanation:

The slopes of perpendicular lines have a product of - 1.

Slope of line that passes through (4, 8) and (2, - 1):

m1 = slope = (-1 - 8) / (2 - 4) = - 9 / (-2) = 9/2

Slope of perpendicular line is m2:

(m1) (m2) = - 1

m2 = - 1/m1 = - 1 / (9/2) = - 2/9

The slope of the perpendicular line is - 2/9

Now we write the expression for the slope of the second line. We use x for the unknown x-coordinate and - 2/9 for the slope.

m2 = (5 - 2) / (-4 - x) = - 2/9

3 / (-4 - x) = - 2/9

Cross multiply:

-2 (-4 - x) = 3 * 9

8 + 2x = 27

2x = 19

x = 19/2