Question

Draw the dilation of ABC using center P and a scale factor of 1/3 Draw the dilation of ABC using center A and a scale factor of 2. . Explain how they are similar.

Answer 1

Let's begin by listing out the information given to us:

$A(5,6),B(5,10),C(8,3)$

A scale factor of 1/3 means the triangle will be smaller (reduction):

$\begin{gathered} P=(2,3) \\ AB=4\Rightarrow A^{\prime}B^{\prime}=\frac{4}{3} \\ BC=\sqrt[]{58}\Rightarrow B^{\prime}C^{\prime}=\frac{\sqrt[]{58}}{3} \\ AC=\sqrt[]{18}\Rightarrow A^{\prime}C^{\prime}=\frac{\sqrt[]{18}}{3}=\sqrt[]{6} \end{gathered}$

A scale factor of 2 means the triangle will be bigger (enlargement):

$\begin{gathered} A^{\prime\prime}=2A=2(5,6)=(10,12) \\ B^{\prime\prime}=2B=2(5,10)=(10,20) \\ C^{\prime\prime}=2C=2(8,3)=(16,6) \end{gathered}$

Both triangles are similar; while the first is a reduction, the second is an enlargement