Question

triangle cat has vertices with coordinates c(-6, 4), a(2, 2), and t(-2, -8). a) dilate △cat using the origin as the center of dilation and a scale - factor of 1/2 to form △dog. b) what are the coordinates of the dilated image? d( o( g(

Explanation:

Step1: Recall dilation rule

When dilating a point $(x,y)$ with the origin as the center of dilation and a scale - factor $k$, the new coordinates $(x',y')$ are given by $(kx,ky)$. Here $k = \frac{1}{2}$.

Step2: Find coordinates of dilated point D (corresponding to C)

For point $C(-6,4)$, using the dilation formula: $x'=\frac{1}{2}\times(-6)= - 3$ and $y'=\frac{1}{2}\times4 = 2$. So $D(-3,2)$.

Step3: Find coordinates of dilated point O (corresponding to A)

For point $A(2,2)$, $x'=\frac{1}{2}\times2 = 1$ and $y'=\frac{1}{2}\times2=1$. So $O(1,1)$.

Step4: Find coordinates of dilated point G (corresponding to T)

For point $T(-2,-8)$, $x'=\frac{1}{2}\times(-2)=-1$ and $y'=\frac{1}{2}\times(-8)= - 4$. So $G(-1,-4)$.

Answer:

$D(-3,2)$
$O(1,1)$
$G(-1,-4)$