Question

Let O , P , and Q be distinct collinear points with PQ=3 . Let P′ and Q′ be the images of points P and Q under dilation from point O with scale factor 4 .

What is the length of the image segment P′Q′ ?

Responses

1. 1

2. 7

3. 9

4. 12

Answer 1

Answer If O, P, and Q are collinear points with PQ = 3, and P' and Q' are the images of P and Q under dilation from O with a scale factor of 4, then the length of the segment P'Q' will be 4 times the length of the segment PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = $\boxed{12}$.

To see why this is the case, recall that a dilation with a scale factor of 4 expands or contracts a figure by a factor of 4 in each direction. In this case, the dilation from O with a scale factor of 4 expands the segment PQ by a factor of 4, resulting in the segment P'Q' with a length of 4 times the length of PQ. Since PQ = 3, the length of P'Q' will be 4 * 3 = 12.