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(−2, 7) and point d(−10, −1), what is another point that could represent a corner of the trail?
(10, 7)
(14, 7)
(12, 7)
(8, 7)

From the coordinate plane, we can see that the enlarged point A refers to point F, and enlarged point D refers to point I. To solve for this problem, we know that the ratios of each side should be similar (both the original and enlarged). Since the given choices have all y values equal to 7, so we have to look for the enlarged point of point G. Let us call that point as point C.

In this case, we take the ratio of side IF and side FG. First solving for length using distance formula:

IF^2 = (2 – 4)^2 + (-4 - -2)^2

IF^2 = 8

IF = sqrt 8

FG^2 = (7 – 4)^2 + (-2 - -2)^2

FG^2 = 9

FG = 3

Therefore the ratio of IF/FG must be equal to the ratio of DA / AC:

IF / FG = DA / AC

Find DA first:

DA^2 = (-10 - -2)^2 + (-1 -7)^2

DA^2 = 128

DA = sqrt 128

So,

sqrt 8 / 3 = sqrt 128 / AC

AC = 12

Finding for point C:          y  of point C = 7

AC^2 = (x - -2)^2 + (7 – 7)^2

12^2 = (x + 2)^2

x + 2 = 12

x = 10

(10, 7)

the answers are in the images, i received 100% on this assignment. hope this !