Question

wxyz and hijk are shown on the coordinate grid, where wxyz is a dilation of hijk. 6. complete the table.

segment	slope	distance
$overline{jk}$	0	3
$overline{wx}$	2/2 = 1	$2sqrt{2}$
$overline{hi}$	3/3 = 1	$3sqrt{2}$

1. show the dilation on the coordinate grid by drawing dotted lines from the center of dilation through each vertex. 8. write a description of the dilation by giving the center of dilation and the scale factor.

Explanation:

Step1: Recall slope formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line, $y_2=y_1$, so slope $m = 0$. For non - horizontal lines, we calculate as follows.

Step2: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step3: Calculate for $\overline{YZ}$

Assume $Y(x_1,y_1)$ and $Z(x_2,y_2)$ are on a horizontal line. Let $Y(3, - 1)$ and $Z(1,-1)$. Slope $m=\frac{-1-(-1)}{3 - 1}=0$. Distance $d=\sqrt{(3 - 1)^2+(-1+1)^2}=\sqrt{4+0}=2$.

Step4: Calculate for $\overline{JK}$

Let $J(5,-4)$ and $K(2,-4)$. Slope $m=\frac{-4-(-4)}{5 - 2}=0$. Distance $d=\sqrt{(5 - 2)^2+(-4 + 4)^2}=3$.

Step5: Calculate for $\overline{WX}$

Let $W(0,-2)$ and $X(2,0)$. Slope $m=\frac{0+2}{2 - 0}=1$. Distance $d=\sqrt{(2 - 0)^2+(0 + 2)^2}=\sqrt{4 + 4}=2\sqrt{2}$.

Step6: Calculate for $\overline{HI}$

Let $H(-3,-5)$ and $I(0,-2)$. Slope $m=\frac{-2+5}{0+3}=1$. Distance $d=\sqrt{(0 + 3)^2+(-2 + 5)^2}=\sqrt{9+9}=3\sqrt{2}$.

Answer:

Segment	Slope	Distance
$\overline{JK}$	0	3
$\overline{WX}$	1	$2\sqrt{2}$
$\overline{HI}$	1	$3\sqrt{2}$