Question

The vertices of a figure are given. Draw the figure and its image after a dilation with the given scale factor. Identify the type of dilation.

$\mathrm{B}(3,3),\mathrm{C}(3,6),\mathrm{D}(6,6),\mathrm{E}(6,3);\mathrm{k}=\frac{1}{3}$

Answer 1

Step 1:Find the coordinates of image after dilation.

Given, coordinates and scale factor is $\mathrm{B}(3,3),\mathrm{C}(3,6),\mathrm{D}(6,6),\mathrm{E}(6,3);\mathrm{k}=\frac{1}{3}$.

Using the above criteria of dilation.

$$\begin{gathered} \mathrm{B}(3,3)=\mathrm{B}\text{'}(3\times \frac{1}{3},3\times \frac{1}{3})=\mathrm{B}\text{'}(1,1) \\ \mathrm{C}(3,6)=\mathrm{C}\text{'}(3\times \frac{1}{3},6\times \frac{1}{3})=\mathrm{C}\text{'}(1,2) \\ \mathrm{D}(6,6)=\mathrm{D}\text{'}(6\times \frac{1}{3},6\times \frac{1}{3})=\mathrm{D}\text{'}(2,2) \\ \mathrm{E}(6,3)=\mathrm{E}\text{'}(6\times \frac{1}{3},3\times \frac{1}{3})=\mathrm{E}\text{'}(2,1) \end{gathered}$$

Step 2: Plot the graph.

Step 3: Final answer.

Hence, the coordinates of image after dilation is $\mathrm{B}\text{'}(1,1),\mathrm{C}\text{'}(1,2),\mathrm{D}\text{'}(2,2),\mathrm{E}\text{'}(2,1)$.