Question

for the set of triangle vertices, find the coordinates of the vertices of the image after a dilation of the triangle by the given scale factor. then graph the pre - image and image on a separate sheet of paper.
j(-8, 0), k(-4, 4), l(-2, 0), k = 0.5

Explanation:

Step1: Recall dilation formula

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

Step2: Find coordinates of $J'$

Given $J(-8,0)$ and $k = 0.5$.
$x_J'=0.5\times(-8)=-4$
$y_J'=0.5\times0 = 0$
So $J'(-4,0)$.

Step3: Find coordinates of $K'$

Given $K(-4,4)$ and $k = 0.5$.
$x_K'=0.5\times(-4)=-2$
$y_K'=0.5\times4 = 2$
So $K'(-2,2)$.

Step4: Find coordinates of $L'$

Given $L(-2,0)$ and $k = 0.5$.
$x_L'=0.5\times(-2)=-1$
$y_L'=0.5\times0 = 0$
So $L'(-1,0)$.

Answer:

$J'(-4,0)$
$K'(-2,2)$
$L'(-1,0)$