Question

Find and graph the image of quadrilateral PQRS after a dilation centered at the origin with a scale factor of ¼. P(0, -4), Q(8,-4), R(8, -8), S(0, -8).

Answer 1

If the point (x, y) is dilated about the origin by a scale factor of k, then its image will be (k x, k y), which means we will multiply each coordinate by the scale factor.

Since the vertices of the quadrilateral PQRS are

P = (0, -4)

Q = (8, -4)

R = (8, -8)

S = (0, -8)

Since the scale factor of dilation is 1/4, then

Multiply the coordinates of each point by 1/4 to find the image of it.

$\begin{gathered} P^{\prime}=(0\times\frac{1}{4},-4\times\frac{1}{4}) \\ \\ P^{\prime}=(0,-1) \end{gathered}$$\begin{gathered} Q^{\prime}=(8\times\frac{1}{4},-4\times\frac{1}{4}) \\ \\ Q^{\prime}=(2,-1) \end{gathered}$$\begin{gathered} R^{\prime}=(8\times\frac{1}{4},-8\times\frac{1}{4}) \\ \\ R^{\prime}=(2,-2) \end{gathered}$$\begin{gathered} S^{\prime}=(0\times\frac{1}{4},-8\times\frac{1}{4}) \\ \\ S^{\prime}=(0,-2) \end{gathered}$

Now, we can graph them