Verified answer

Two perpendicular lines' slopes are the additive and multiplicative inverse of one another; for instance,

2 => -1/2

First, determine the slope of the line whose coordinates you know.

y2-y1/x2-x1 = 11 - 7 / 1 - 4

= 4 / -3

If the slope of the other line is perpendicular, then we find the additive and multiplicative inverse:

4 / -3 ======> -3 / 4 =========> 3 / 4

so, the slope of the line whose x-coordinate we're looking for is 3 / 4.

Slope formula again:

y2-y1/x2-x1 = 13 / -6 - x = 3 / 4

13 / (-6 - x) = 3 / 4

13 = -18/4 - 3/4x

70/4 = -3/4x

x = -70/3