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 pre - image and image on a separate sheet of paper. s(0, 0), t(-4, 0), v(-8, -8), k = 1.25, 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 new coordinates of point $S$

Given $S(0,0)$ and $k = 1.25$.
$x'=1.25\times0 = 0$, $y'=1.25\times0 = 0$. So the new coordinates of $S$ are $(0,0)$.

Step3: Find new coordinates of point $T$

Given $T(- 4,0)$ and $k = 1.25$.
$x'=1.25\times(-4)=-5$, $y'=1.25\times0 = 0$. So the new coordinates of $T$ are $(-5,0)$.

Step4: Find new coordinates of point $V$

Given $V(-8,-8)$ and $k = 1.25$.
$x'=1.25\times(-8)=-10$, $y'=1.25\times(-8)=-10$. So the new coordinates of $V$ are $(-10,-10)$.

Answer:

$S(0,0)$
$T(-5,0)$
$V(-10,-10)$