Question

Select the correct answer from the drop-down menu. has vertices at , , and . The triangle is dilated by a factor of 3 with the center of dilation at vertex B, resulting in . What is ? Round to the nearest hundredth. units

Answer 1

Notice that, since B is the center of dilation, B'=B. Furthermore, is a dilation all the distances are enlarged by a factor equal to the dilation factor; thus,

`\Rightarrow B^(\prime)C^(\prime)=3\cdot BC`

Calculate BC using the formula below,

`\begin{gathered} P_1=(x_1,y_1),P_2=(x_2,y_2)_{} \\ \Rightarrow\text{distance}(P_1,P_2)=\sqrt[]{(x_1-x_2)^2+(y_1-y_2_{})^2} \end{gathered}`

Therefore,

`\Rightarrow\text{distance}(BC)=\sqrt[]{(4-1)^2+(8-(-2))^2}=\sqrt[]{9+100}=\sqrt[]{109}`

Hence,

`\begin{gathered} \Rightarrow B^(\prime)C^(\prime)=3\sqrt[]{109}=31.320919\ldots \\ \Rightarrow B^(\prime)C^(\prime)\approx31.32 \end{gathered}`

The answer is B'C'=31.32