Question

Question 3: Quadrilateral A'B'C'E' is the image of quadrilateral ABCE after a dilation centered

Answer 1

Answer: Scale factor = 1/2 = 0.5

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Explanation:

We have AB = 3 and A'B' = 1.5; the ratio between the two segment lengths is (A'B')/(AB) = (1.5)/(3) = 1/2 = 0.5

Similarly,

• (B'C')/(BC) = (3)/(6) = 1/2 = 0.5
• (C'E')/(CE) = (2.5)/(5) = 1/2 = 0.5

You only need to pick one of these statements to be able to find the scale factor. The scale factor of 1/2 or 0.5 indicates that the image is half as small compared to the preimage. More specifically, each segment of the image is half as small compared to the corresponding segment on the preimage.

• A'B' is half as small as AB
• B'C' is half as small as BC
• C'E' is half as small as CE
• A'E' is half as small as AE

We don't have numbers for AE and A'E', but the last statement above must be true because the dilation applies to all segment lengths.