The vertices of a parallelogram are shown below.

(0 , 0), (18 , 0), (24 , 30), (6 , 30)

Which of the following points is a vertex for the image produced by a dilation about the origin with a scale factor of ?
A. (21 , 3)

B. (10 , 6)

C. (2 , 10)

D. (12 , 0)

1 answer

To perform a dilation about the origin with a scale factor of k, each coordinate (x, y) of a point is multiplied by k.

In this case, let's consider the dilation with a scale factor of k = 2.

For the point (0, 0), the dilation will just be (0, 0) because any point multiplied by 2 will still be at the origin.

For the point (18, 0), the x-coordinate is multiplied by 2, giving us (36, 0).

For the point (24, 30), both the x and y-coordinates are multiplied by 2, giving us (48, 60).

For the point (6, 30), the x-coordinate is multiplied by 2, giving us (12, 30).

Out of the given options, the point (12, 0) is a vertex of the image produced by the dilation about the origin with a scale factor of 2.

Therefore, the correct answer is D. (12, 0).