Question

Rectangle ABCD is dilated by scale factor 2.5 and a center of dilation at the origin. What are the coordinates of vertex A'?

Responses

A(0,−5)

B(-5,5)


C(-5, 0)


D(5,-5)

Answer 1

Explanation:

Original coordinates of A: A(0, -5)

Scale factor: 2.5

Coordinates of A':

x-coordinate of A' = x-coordinate of A * Scale factor = 0 * 2.5 = 0

y-coordinate of A' = y-coordinate of A * Scale factor = -5 * 2.5 = -12.5

So, the coordinates of vertex A' are A'(0, -12.5).

Therefore, none of the provided options (A, B, C, or D) matches the correct coordinates of vertex A' after the dilation. The correct answer is A'(0, -12.5).

Answer 2

B

Explanation:

since the dilatation is centred at the origin, then multiply each of the original coordinates by the scale factor 2.5

from the diagram

A (- 2, 2 ) , then

A' (2.5(- 2), 2.5(2) ) → A' (- 5, 5 )