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: Identify the coordinates of point T

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

Step2: Apply the dilation formula

When dilating a point $(x,y)$ with a scale - factor $k$ and center of dilation at the origin $(0,0)$, the new coordinates $(x',y')$ are given by $(kx,ky)$. Here, $k = \frac{1}{2}$, $x=-6$ and $y = 2$.
$x'=\frac{1}{2}\times(-6)=-3$
$y'=\frac{1}{2}\times2 = 1$

Answer:

$(-3,1)$