Our first step will be to draw lines from the center P to each vertex of RSTU. Because the scale factor is less than 1, this dilation is a reduction and the image R'S'T'U' will be smaller than RSTU.
To dilate this by 13, we are going to do a neat trick. Let's copy PU using a compass. Open up the compass to the width of PU and then use this compass setting to mark an identical segment AC underneath.
Next, place an arbitrary point D that is not on AC, and draw a line through it using a straightedge.
Use a compass to measure the distance between A and D and then extend that distance three times along the segment we just drew.
Connect F and C with a straightedge.
By drawing a parallel segment to FC from D, we can cut AC in two smaller segments where one of them is 13 of the length of AC and the other is 23. Use a compass to draw a pair of identical arcs around D and F.
Adjust the width of your compass to measure the angle at F and copy that angle around D.
The segment through D, and the intersection of the arcs, is parallel to FC.
Now that we know how long 13 of AC is, we can use this to restrict PU. Again, we have to use our compass.
If we repeat this procedure for the remaining sides, we can get all vertices of the dilated quadrilateral.
