Question

A dilation with a scale factor of 2 is applied to the three line segments shown. The resulting images are P′Q′⎯⎯⎯⎯⎯⎯⎯⎯ , A′B′⎯⎯⎯⎯⎯⎯⎯ , and M′N′⎯⎯⎯⎯⎯⎯⎯⎯⎯ .

What are the lengths of the images?

Drag the answer into the box to match each segment.

Answer 1

Answer: P' Q' = 8 cm

A' B' = 6 cm

M' N' = 12 cm

Explanation:

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Answer 2

Applying a scale factor means by definition to multiply the lengths of the segments by the scale factor. If the scale factor is larger than 1, we call it a dilation.

Now, we get that AB has a length of 1.5 cm; applying the scale factor yields a new segment with 2 new endpoints that has a length of A'B'=3 cm = 1.5cm*2

Similarly, we get that since PQ=2 cm, P'Q'=2cm*2=4cm and finally since MN=3 cm, M'N'=6 cm.