Question

What is the image of Q for a dilation with the center (0,0) and a scale factor of 0.5?

A.) (0.5, 2.5)
B.) (2, 10)
C.) (1, 2.5)
D.) (10, 2)

Answer 1

Answer: OPTION A.

Explanation:

A dilation is defined as a transformation in which the Image (The figure obtained after the transformation) and the Pre-Image (The original figure before the transformation) have the same shape, but they have different sizes.

In this case you know that the dilation is centered at the origin and the scale factor is:

`k=0.5`

Therefore, the rule is the following:

`Q(kx,ky)`

You can identify in the figure attached that the point Q is:

`Q(1,5)`

Therefore, you must multiply its coordinates by the scale factor 0.5 in order to get its Image Q'. This is:

`Q'=(1*0.5,5*0.5)\\\\Q'=(0.5.2.5)`