Given E (-6, y), F(6, 13)G(14,11), and H(8.-13), find the value of y so that EF
is perpendicular to GH.

  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.