Question

In the image below, point C lies on segment RS. Use your ruler to help dilate RS using C as a center with a scale factor of 1/2. Label the image segment R'S'. Using your ruler, give the measurements of segment RS and segment R'S' in inches and verify that R'S' = 1/2 RS.

Answer 1

If we have a segment RS and a point C that lies in the segment, and we have to apply a dilation with scale factor k=1/2 with point C as center of dilation, we have to start by measuring RS.

The measurements are:

RS = 87 mm

RC = 37 mm

CS = 50 mm

Then, if C is the center of dilation, it will stay in the same position.

The segment R'C will have half the length of RC, because the dilation factor is 1/2, so we will have R'C=37/2=18.5 mm.

Point C, as it is the center of dilation, will stay in the same position, and R' will be at 18.5 mm from C, at the left.

The segment CS' will also have half the length of CS, so its length will be CS'=50/2=25 mm.

Point C will stay in the same coordinates and S' will be 25 mm from C.

This dilation will have R' located as the midpoint of segment RC and S' as the midpoint of segment CS.

We can see it in the graph: