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.

$\mathrm{P}(-3,-2),\mathrm{Q}(-3,0),\mathrm{R}(0,0);\mathrm{k}=4$

Answer 1

Find the coordinates of image after dilation.

Given, coordinates and scale factor, $\mathrm{P}(-3,-2),\mathrm{Q}(-3,0),\mathrm{R}(0,0);\mathrm{k}=4$

As we know in dilation with scale factor $\mathrm{k}$ coordinates changes as:

$\mathrm{A}(\mathrm{x},\mathrm{y})=\mathrm{A}\text{'}(\mathrm{x}\times \mathrm{k},\mathrm{y}\times \mathrm{k})$

Using the above criteria of dilation:

$$\begin{gathered} \mathrm{P}(-3,-2)=\mathrm{P}\text{'}(-3\times 4,-2\times 4)=\mathrm{P}\text{'}(-12,-8) \\ \mathrm{Q}(-3,0)=\mathrm{Q}\text{'}(-3\times 4,0\times 4)=\mathrm{Q}\text{'}(-12,0) \\ \mathrm{R}(0,0)=\mathrm{R}\text{'}(0\times 4,0\times 4)=\mathrm{R}\text{'}(0,0) \end{gathered}$$

Hence, the coordinates of image after dilation is $\mathrm{P}\text{'}(12,-8),\mathrm{Q}\text{'}(-12,0),\mathrm{R}\text{'}(0,0)$.