Question

the figure below is dilated with the center of dilation at the origin and a scale factor of $\frac{1}{2}$. what are the coordinates of the image of point t after this transformation?

Explanation:

Step1: Determine the original coordinates of point T

From the graph, the coordinates of point T are $(-6,2)$.

Step2: Apply the dilation formula

When dilating a point $(x,y)$ with a scale - factor $k$ centered at the origin, the new coordinates $(x',y')$ are given by $(x',y')=(k x,k y)$. Here, $k = \frac{1}{2}$, $x=-6$, $y = 2$. So $x'=\frac{1}{2}\times(-6)=-3$ and $y'=\frac{1}{2}\times2 = 1$.

Answer:

$(-3,1)$