Question

3 dilate triangle abc with a scale factor of 3 with center of dilation (-4,4) click to select polygon def

Explanation:

Step1: Recall dilation formula

If the center of dilation is $(h,k)$ and the scale - factor is $k_{s}$, and a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(h + k_{s}(x - h),k + k_{s}(y - k))$.

Step2: Identify coordinates of points A, B, C

From the graph, $A(-3,3)$, $B(-2,1)$, $C(0,2)$, and the center of dilation $(h,k)=(-4,4)$ and $k_{s}=3$.

Step3: Calculate new coordinates of A

For point $A(-3,3)$:
$x'=-4+3(-3 + 4)=-4 + 3\times1=-1$
$y'=4+3(3 - 4)=4+3\times(-1)=1$
So, $A'(-1,1)$.

Step4: Calculate new coordinates of B

For point $B(-2,1)$:
$x'=-4+3(-2 + 4)=-4+3\times2 = 2$
$y'=4+3(1 - 4)=4+3\times(-3)=4 - 9=-5$
So, $B'(2,-5)$.

Step5: Calculate new coordinates of C

For point $C(0,2)$:
$x'=-4+3(0 + 4)=-4+3\times4=8$
$y'=4+3(2 - 4)=4+3\times(-2)=4 - 6=-2$
So, $C'(8,-2)$.

Answer:

The new triangle has vertices $A'(-1,1)$, $B'(2,-5)$, $C'(8,-2)$