# How do you dilate a rectangle with points (6,3), (2,3) (6,9) (2,9) by a scale factor of .5 with 6,3 as the center of dilation?

Jun 8, 2018

color(maroon)("Coordinates of the dilated rectangle are "

color(crimson)((6,3), (4,3), (6,7), (4,7)

#### Explanation:

$A \left(6 , 3\right) , B \left(2 , 3\right) , C \left(6 , 9\right) , D \left(2 , 9\right) , \text{ dilated about " E(6,3) " by factor } \frac{1}{2}$

$A ' \left(\begin{matrix}x \\ y\end{matrix}\right) = .5 a + .5 e = .5 \cdot \left(\begin{matrix}6 \\ 3\end{matrix}\right) + .5 \cdot \left(\begin{matrix}6 \\ 3\end{matrix}\right) = \left(\begin{matrix}6 \\ 3\end{matrix}\right)$

$B ' \left(\begin{matrix}x \\ y\end{matrix}\right) = .5 b + .5 e = .5 \cdot \left(\begin{matrix}2 \\ 3\end{matrix}\right) + .5 \cdot \left(\begin{matrix}6 \\ 3\end{matrix}\right) = \left(\begin{matrix}4 \\ 3\end{matrix}\right)$

$C ' \left(\begin{matrix}x \\ y\end{matrix}\right) = .5 c + .5 e = .5 \cdot \left(\begin{matrix}6 \\ 9\end{matrix}\right) + .5 \cdot \left(\begin{matrix}6 \\ 3\end{matrix}\right) = \left(\begin{matrix}6 \\ 7\end{matrix}\right)$

$D ' \left(\begin{matrix}x \\ y\end{matrix}\right) = .5 d + .5 e = .5 \cdot \left(\begin{matrix}2 \\ 9\end{matrix}\right) + .5 \cdot \left(\begin{matrix}6 \\ 3\end{matrix}\right) = \left(\begin{matrix}4 \\ 7\end{matrix}\right)$

color(maroon)("Coordinates of the dilated rectangle are "

color(crimson)((6,3), (4,3), (6,7), (4,7)