Finding the scale factor from endpoints

Question

Segment M'N' is a dilation of segment MN. The endpoints of MN are M(2,5) and N(8,0) and the endpoints of M' N' are M' (5,12.5) and N' (20,0). Find the scale factor of the dilation and classify it as an enlargement or as a reduction.

Answer 1

To find the length of a segment given two points, you can use the formula √[(X₂-X₁)² +(Y₂-Y₁)²] which is a manipulation of the Pythagorean theorum. You can pick either point as X₂, Y₂ but be consistent.

Our first line MN is √[(8-2)²+(0-5)²] -> √[6²+5²]=√(36+25)=√61=7.81 Approximately

For M'N' we get √[(20-5)²+(0-12.5)²]=√(15²+12.5²)=√(225+156.25)=√381.25)=19.53

 

To find the scale factor, we divide the New value M'N' by the original value MN to get

19.53/7.81≅≈2.5 as your answer. Because it's greater than 1, you know the new value is larger and is classified now as an enlargement.