Question

I need to know the scale factor and what S is.

Answer 1

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:

`\text{scale factor}=(PR)/(PT)=(27)/(9)=3`

Now that we have the scale factor, we can find the length of PS by comparing it with the corresponding side PQ:

`\begin{gathered} \text{scale factor}=(PQ)/(PS) \\ 3=(24)/(PS) \\ PS=(24)/(3)=8 \end{gathered}`

If the length of PS is 8 units and S is above the x-axis to the right, its coordinates will be (8, 0).