Question

name: cody king date:02-09-26
6.
graph the dilated image of triangle xyz using a scale factor of 1.5 and (0,0) as the center of dilation.
x: ____ x: ____
y: ____ y: ____
z: ____ z: ____

Explanation:

Step1: Identify original coordinates

From the graph:
$X: (-4, 3)$
$Y: (6, 0)$
$Z: (-4, -2)$

Step2: Apply dilation formula

Dilation with center $(0,0)$ and scale factor $k=1.5$ uses $(x', y') = (k \times x, k \times y)$.
For $X'$:
$x' = 1.5 \times (-4) = -6$, $y' = 1.5 \times 3 = 4.5$
For $Y'$:
$x' = 1.5 \times 6 = 9$, $y' = 1.5 \times 0 = 0$
For $Z'$:
$x' = 1.5 \times (-4) = -6$, $y' = 1.5 \times (-2) = -3$

Answer:

X: $(-4, 3)$
X': $(-6, 4.5)$
Y: $(6, 0)$
Y': $(9, 0)$
Z: $(-4, -2)$
Z': $(-6, -3)$

(To graph the dilated triangle, plot points $X'(-6, 4.5)$, $Y'(9, 0)$, $Z'(-6, -3)$ and connect them to form $\triangle X'Y'Z'$)