Question

A dilation from center O with scale factor r1=14 maps a point P to another point P′ . Then a second dilation from O with scale factor r2 maps P′ to P .

What is the value of r2 ?

Answer 1

The scale factor r2 that maps point P' back to point P after an initial dilation with scale factor r1=14 is 1/14, since the product of the two scale factors must equal 1 to return to the original size.

Step-by-step explanation:

A student has asked about the value of the scale factor r2 in a sequence of dilations with a center O. The point P is first mapped to P' using a scale factor r1 = 14, followed by a second dilation mapping P' back to P using scale factor r2.

To find r2, we must understand that the dilation which maps P to P' is inverted by the second dilation. This means the product of the two scale factors, r1 and r2, should be equal to 1, as we are ultimately returning to the original size.

Given that r1 is 14, we set up the equation r1 * r2 = 1, and solving for r2 gives us r2 = 1/14. Thus, the second scale factor, r2, that maps P' back to P is 1/14.