Question

1. rhombus jklm with vertices j(-10, 2), k(-2, 8), l(6, 2), and m(-2, -4): k = 1/2
2. triangle wxy with vertices w(-4, 8), x(10, 0), and y(-2, -8): k = 1/4

Explanation:

Step1: Recall dilation formula

For a point $(x,y)$ dilated by a scale - factor $k$ about the origin, the new point $(x',y')$ is given by $(x',y')=(k x,k y)$.

Step2: Dilate vertices of rhombus $JKLM$

For point $J(-10,2)$ with $k = \frac{1}{2}$, $J'=(\frac{1}{2}\times(-10),\frac{1}{2}\times2)=(-5,1)$.
For point $K(-2,8)$ with $k=\frac{1}{2}$, $K'=(\frac{1}{2}\times(-2),\frac{1}{2}\times8)=(-1,4)$.
For point $L(6,2)$ with $k = \frac{1}{2}$, $L'=(\frac{1}{2}\times6,\frac{1}{2}\times2)=(3,1)$.
For point $M(-2,-4)$ with $k=\frac{1}{2}$, $M'=(\frac{1}{2}\times(-2),\frac{1}{2}\times(-4))=(-1,-2)$.

Step3: Dilate vertices of triangle $WXY$

For point $W(-4,8)$ with $k=\frac{1}{4}$, $W'=(\frac{1}{4}\times(-4),\frac{1}{4}\times8)=(-1,2)$.
For point $X(10,0)$ with $k=\frac{1}{4}$, $X'=(\frac{1}{4}\times10,\frac{1}{4}\times0)=(2.5,0)$.
For point $Y(-2,-8)$ with $k=\frac{1}{4}$, $Y'=(\frac{1}{4}\times(-2),\frac{1}{4}\times(-8))=(-0.5,-2)$.

Answer:

The dilated vertices of rhombus $JKLM$ are $J'(-5,1),K'(-1,4),L'(3,1),M'(-1,-2)$ and the dilated vertices of triangle $WXY$ are $W'(-1,2),X'(2.5,0),Y'(-0.5,-2)$