Question

Line segment ab is dilated to create line segment a'b' using point q as the center of dilation. What is the scale factor? 1 1. 25 2 2. 5.

Answer 1

Dilation involves changing the size of a line segment

The scale factor is 2

From the question (see attachment), we have the following side lengths

$AQ = 1.25$

$A'Q' = 1.25 + 1.25$

$A'Q' = 2.5$

So, the scale factor (k) from AB to A'B' is calculated using the following scale factor formula

$k = \frac{A'Q'}{AQ}$

This gives

$k = \frac{2.5}{1.25}$

Divide 2.5 by 1.25

$k = 2$

Hence, the scale factor is 2

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