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,
[tex]\text{Scale factor}=\dfrac{\text{Side length of image}}{\text{Corresponding side of original figure}}[/tex]
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.
[tex]4=\dfrac{P'Q'}{PQ}[/tex]
It is given that PQ=3.
[tex]4=\dfrac{P'Q'}{3}[/tex]
Multiply both sides by 3.
[tex]4\times 3=P'Q'[/tex]
[tex]12=P'Q'[/tex]
Therefore, the length of the image segment P'Q' is 12 units.
A segment in the image is proportionally longer or shorter than the corresponding one in the pre-image.
Given Information:
Solution:
Scale factor=Side length of image/corresponding side of original figure
Segment P'Q' is the image of segment PQ and the scale factor is 4.
4=P'Q'/ PQ
It is given that PQ=3
4=P'Q'/3
Multiply both sides by 3.
4*3=P'Q'
12=P'Q'
Therefore, the length of the image segment P'Q' is 12 units.
Learn more about segment, refer to the link:
https://brainly.com/question/18104026
