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′?

Given:

O, P, and Q be distinct collinear points with PQ=3.

P′ and Q′ be the images of points P and Q under dilation from point O with scale factor 4.

To find:

The length of the image segment P'Q'.

Solution:

We know that,

P′ and Q′ be the images of points P and Q under dilation from point O with scale factor 4. So, Segment P'Q' is the image of segment PQ and the scale factor is 4.

It is given that PQ=3.

Multiply both sides by 3.

Therefore, the length of the image segment P'Q' is 12 units.