Question

quadrilateral math has vertices m=(1,3), a=(-4,6), t=(-2,7), and h=(5,9). quadrilateral math is the image after dilating math by a scale factor of 3 about the origin. what are the coordinates of a? a. (-4,18) b. (-12,6) c. (-12,18) d. (-64,216)

Explanation:

Step1: Recall dilation formula

When dilating a point $(x,y)$ by a scale factor $k$ about the origin, the new - point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$. Here, $k = 3$ and the point $A=(-4,6)$.

Step2: Calculate new coordinates

For the $x$ - coordinate of $A'$, $x'=3\times(-4)=-12$. For the $y$ - coordinate of $A'$, $y'=3\times6 = 18$. So the coordinates of $A'$ are $(-12,18)$.

Answer:

C. $(-12,18)$