Parallelogram fghi on the coordinate plane below represents the drawing of a horse trail through a local park.

in order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. if two corners of the trail are at point a (3, 8) and point d (1, 2), what is another point that could represent a corner of the trail?

a)(13, 8)

b)(10, 8)

c)(8, 8)

d)(6, 8)

The answer is A)(13, 8).

Distance I to F is:     yf - yi = -1 - (-4) = -1 + 4 = 3
Distance D to A is:   ya - yd = 8 - 2 = 6

Distance D to A : Distance I to F = 6 : 3
6 : 3 = 2, so scale factor is 2.

Among all choices, we see that the y point of another corner is 8, so we need to find x point.

Distance I to H is:                 xh - xi = -2 - (-7) = -2 + 7 = 5
Distance A to x corner is:    x - xa = x - 3

Since Distance I to H is 5, and scale factor is 2, we have:
Distance A to x corner : Distance I to H = 2
Distance A to x corner = 2 * Distance I to H = 2 * 5 = 10

Distance A to x corner is:    xa - x = x - 3 = 10
x - 3 = 10
x = 10 + 3
x = 13