Question

Center of Dilation1. Dilate Figure PQRS by a scale factor of using the point (4, 6)as the center of dilation. Determine the coordinates of FigureP'Q'R'S' and draw the approximate dilation on the coordinateplane.8th grade pre algebra

Answer 1

Answer:

The coordinates of P',Q',R',S' are;

$\begin{gathered} P^{\prime}=(-6.5,6) \\ Q^{\prime}=(1,6) \\ R^{\prime}=(4,-7.5) \\ S^{\prime}=(-9.5,-7.5) \end{gathered}$

Explanation:

Given the quadrilateral PQRS as shown on the diagram.

To determine the coordinates of the figure P'Q'R'S' which is the dilated image of PQRS. Let us apply the formula below;

$D_{o,k}(x,y)=(k(x-a)+a,k(y-b)+b)$

Where;

the center of dilation is (a,b)

the scale factor is k

Given;

$\begin{gathered} (a,b)=(4,6) \\ k=\frac{3}{2} \end{gathered}$

And from the image PQRS;

$\begin{gathered} P=(-3,6) \\ Q=(2,6) \\ R=(4,-3) \\ S=(-5,-3) \end{gathered}$

We can then calculate the coordinates of their respective P',Q',R' and S' using the formula;

$\begin{gathered} P^{}=(-3,6) \\ P^{\prime}=(\frac{3}{2}(-3-4)+4,\frac{3}{2}(6-6)+6) \\ P^{\prime}=(\frac{-21}{2}+4,0+6) \\ P^{\prime}=(-6.5,6) \end{gathered}$$\begin{gathered} Q=(2,6) \\ Q^{\prime}=(\frac{3}{2}(2-4)+4,\frac{3}{2}(6-6)+6) \\ Q^{\prime}=(\frac{-6}{2}+4,0+6) \\ Q^{\prime}=(1,6) \end{gathered}$$\begin{gathered} R=(4,-3) \\ R^{\prime}=(\frac{3}{2}(4-4)+4,\frac{3}{2}(-3-6)+6) \\ R^{\prime}=(0+4,\frac{-27}{2}+6) \\ R^{\prime}=(4,-7.5) \end{gathered}$$\begin{gathered} S=(-5,-3) \\ S^{\prime}=(\frac{3}{2}(-5-4)+4,\frac{3}{2}(-3-6)+6) \\ S^{\prime}=(\frac{-27}{2}+4,\frac{-27}{2}+6) \\ S^{\prime}=(-9.5,-7.5) \end{gathered}$

Therefore, the coordinates of P',Q',R',S' are;

$\begin{gathered} P^{\prime}=(-6.5,6) \\ Q^{\prime}=(1,6) \\ R^{\prime}=(4,-7.5) \\ S^{\prime}=(-9.5,-7.5) \end{gathered}$