Question

△xyz is the image of △xyz after a dilation by a scale factor of $\frac{2}{3}$, with the origin as the center of dilation. plot △xyz. > use the graphing tool to plot the triangle. polygon + move undo redo × reset

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated by a scale - factor $k$ with the origin $(0,0)$ as the center of dilation, the new point $(x',y')$ is given by $(x',y')=k(x,y)$.

Step2: Identify coordinates of $\triangle XYZ$

Let's assume the coordinates of $X=( - 8,6)$, $Y=( - 6,-8)$, $Z=(8,-8)$.

Step3: Calculate coordinates of $\triangle X'Y'Z'$

For point $X$:
$x_{X'}=\frac{2}{3}\times(-8)=-\frac{16}{3}\approx - 5.33$, $y_{X'}=\frac{2}{3}\times6 = 4$. So $X'=(-\frac{16}{3},4)$.
For point $Y$:
$x_{Y'}=\frac{2}{3}\times(-6)=-4$, $y_{Y'}=\frac{2}{3}\times(-8)=-\frac{16}{3}\approx - 5.33$. So $Y'=(-4,-\frac{16}{3})$.
For point $Z$:
$x_{Z'}=\frac{2}{3}\times8=\frac{16}{3}\approx5.33$, $y_{Z'}=\frac{2}{3}\times(-8)=-\frac{16}{3}\approx - 5.33$. So $Z'=(\frac{16}{3},-\frac{16}{3})$.

Step4: Plot the points

Use the graphing tool to plot the points $X'(-\frac{16}{3},4)$, $Y'(-4,-\frac{16}{3})$, and $Z'(\frac{16}{3},-\frac{16}{3})$ and connect them to form $\triangle X'Y'Z'$.

Answer:

Plot the points $X'(-\frac{16}{3},4)$, $Y'(-4,-\frac{16}{3})$, $Z'(\frac{16}{3},-\frac{16}{3})$ and connect them to form the triangle.