Question

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)

Answer 1

x = 19/2

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