Question

if the figure shown on the grid below is dilated by a scale factor of 2 with the center of dilation at (-2, -3), what is the coordinate of point c after the dilation?

Explanation:

Step1: Find vector from center to point C

Let the center of dilation $O(-2,-3)$ and point $C(-5,0)$. The vector $\overrightarrow{OC}=(-5 - (-2),0 - (-3))=(-3,3)$.

Step2: Multiply vector by scale - factor

Multiply the vector $\overrightarrow{OC}$ by the scale factor of 2. $2\overrightarrow{OC}=2(-3,3)=(-6,6)$.

Step3: Find new coordinates of point C

To find the new coordinates of point $C'$, add the new vector to the center of dilation coordinates. Let the new coordinates of $C'$ be $(x,y)$. Then $x=-2+(-6)= - 8$ and $y=-3 + 6=3$.

Answer:

$(-8,3)$