Question

he rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A prime, point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?

On a coordinate plane, rectangle A prime B prime C prime D prime has points (negative 10, 8), (negative 6, 8), (negative 6, negative 2), (negative 10, negative 2). Point A is at (negative 4, 3.2).
The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).
The scale factor is 0.4 and the coordinates of point C are (–2.4, –0.8).
The scale factor is 2.5 and the coordinates of point C are (–15, 5).
The scale factor is 0.4 and the coordinates of point C are (–15, 5).

Answer 1

Scale factor = 2.5.

Since the center is the origin, A' = k·A so k = -10 / -4 = 8 / 3.2 = 2.5. For C, C' = (-6, -2), so C = C' / k = (-6/2.5, -2/2.5) = (-2.4, -0.8).

So choose: scale factor 2.5 and C = (–2.4, –0.8).