Question

what is the image of (-2, 6) after a dilation by a scale factor of $\frac{1}{2}$ centered at the origin?

Explanation:

Step1: Multiply x - coordinate by scale factor

When dilating a point $(x,y)$ centered at the origin by a scale factor $k$, the new $x$-coordinate $x'$ is $x'\ = kx$. Here $x=-2$ and $k = \frac{1}{2}$, so $x'=\frac{1}{2}\times(-2)=-1$.

Step2: Multiply y - coordinate by scale factor

The new $y$-coordinate $y'$ is $y' = ky$. Here $y = 6$ and $k=\frac{1}{2}$, so $y'=\frac{1}{2}\times6 = 3$.

Answer:

$(-1,3)$