Line segmentAB has endpoints A(1, 4) and B(2, 8). A dilation, centered at the origin, is applied to AB⎯⎯⎯⎯⎯. The image has endpoints A′(1/8, 1/2) and B′(1/4, 1).What is the scale factor of the dilation?A. 1/8B. 1/2C. 2D. 8

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EvianaE196773idn EvianaE196773idn

04-11-2022
Mathematics

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Line segmentAB has endpoints A(1, 4) and B(2, 8). A dilation, centered at the origin, is applied to AB⎯⎯⎯⎯⎯. The image has endpoints A′(1/8, 1/2) and B′(1/4, 1).What is the scale factor of the dilation?A. 1/8B. 1/2C. 2D. 8

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BrynnanU19461idn BrynnanU19461idn · Answer 1 · 2022-11-04T06:04:18-04:00

Given the following question:

The scale factor is multiplication, we are already given the before and after of the mutiplication all we have to do is find, what were the points multplied by to equal the last endpoints.

Using the process of elimination:

Option A:

[tex]\begin{gathered} 1\times\frac{1}{8}=\frac{1}{8} \\ 4\times\frac{1}{8}=\frac{1}{2} \\ 2\times\frac{1}{8}=\frac{1}{4} \\ 8\times\frac{1}{8}=1 \\ \text{Using cross mutiplication} \end{gathered}[/tex]

Your answer is option A.

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