Question

for the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale factor and center of dilation. then graph the preimage and image on a separate sheet of paper. d(4, 4), f(0, 0), g(8, 0), k = 0.75, centered at the origin

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Find coordinates of $D'$

For point $D(4,4)$ with $k = 0.75$, we have $x'=0.75\times4 = 3$ and $y'=0.75\times4 = 3$. So $D'(3,3)$.

Step3: Find coordinates of $F'$

For point $F(0,0)$ with $k = 0.75$, we have $x'=0.75\times0 = 0$ and $y'=0.75\times0 = 0$. So $F'(0,0)$.

Step4: Find coordinates of $G'$

For point $G(8,0)$ with $k = 0.75$, we have $x'=0.75\times8 = 6$ and $y'=0.75\times0 = 0$. So $G'(6,0)$.

Answer:

$D'(3,3)$
$F'(0,0)$
$G'(6,0)$