In order to find the scale factor between the triangles, we can compare the sides PR and PT, which are corresponding sides between the triangles.
The side PR has a length of 27 units, and the side PT has a length of 9 units, so we can find the scale factor by dividing one length by the other:
[tex]\text{scale factor}=\frac{PR}{PT}=\frac{27}{9}=3[/tex]
Now that we have the scale factor, we can find the length of PS by comparing it with the corresponding side PQ:
[tex]\begin{gathered} \text{scale factor}=\frac{PQ}{PS} \\ 3=\frac{24}{PS} \\ PS=\frac{24}{3}=8 \end{gathered}[/tex]
If the length of PS is 8 units and S is above the x-axis to the right, its coordinates will be (8, 0).
