Answer:
y = 16
Step-by-step explanation:
The slope of GH is ...
G -H = (14, 11) -(8, -13) = (6, 24) = (Δx, Δy)
slope = Δy/Δx = 24/6 = 4
The perpendicular line through F will have a slope of the negative reciprocal of this, or -1/4. The point-slope form of the equation can be written as ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
The perpendicular line through F is then ...
y -13 = (-1/4)(x -6)
For an x-value of -6, the value of y will be ...
y = (-1/4)(-6 -6) +13 = 12/4 +13 = 16
The value of y so that EF is perpendicular to GH is 16.
