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*(1)/(4),-4*(1)/(4)) \\ \\ P^(\prime)=(0,-1) \end{gathered}`
`\begin{gathered} Q^(\prime)=(8*(1)/(4),-4*(1)/(4)) \\ \\ Q^(\prime)=(2,-1) \end{gathered}`
`\begin{gathered} R^(\prime)=(8*(1)/(4),-8*(1)/(4)) \\ \\ R^(\prime)=(2,-2) \end{gathered}`
`\begin{gathered} S^(\prime)=(0*(1)/(4),-8*(1)/(4)) \\ \\ S^(\prime)=(0,-2) \end{gathered}`

Now, we can graph them