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)=(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