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′?

Answer 1

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,

$\text{Scale factor}=\dfrac{\text{Side length of image}}{\text{Corresponding side of original figure}}$

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.

$4=\dfrac{P'Q'}{PQ}$

It is given that PQ=3.

$4=\dfrac{P'Q'}{3}$

Multiply both sides by 3.

$4\times 3=P'Q'$

$12=P'Q'$

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