Select the coordinates A′ and B′ after dilation of the line segment AB with a scale factor of 1/3 , centered at the origin where the endpoints are A(−6,3) and B(−12,9) .(1 point)

Responses

A) A′(−2,1) and B′(−4,3)

B) A′(−2,1) and B′(−12,9)

C) A′(−18,9) and B′(−36,27)

D) A′(−6,3) and B′(−4,3)

1 answer

To dilate a point, we multiply its coordinates by the scale factor. Since the scale factor is 1/3, we will multiply both the x-coordinate and y-coordinate by 1/3.

For point A(−6,3), multiplying by 1/3 gives:

A' = (-6 * (1/3), 3 * (1/3))
A' = (-2, 1)

For point B(−12,9), multiplying by 1/3 gives:

B' = (-12 * (1/3), 9 * (1/3))
B' = (-4, 3)

Therefore, the correct answer is:

A) A′(−2,1) and B′(−4,3)