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: Find the original coordinates of point T

From the graph, the coordinates of point T are \((-4,2)\).

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated with center at the origin and scale factor \(k\), the new coordinates \((x',y')\) are given by \((x',y')=(k\times x,k\times y)\). Here \(k = \frac{1}{2}\), \(x=-4\), \(y = 2\).
So \(x'=\frac{1}{2}\times(-4)=-2\) and \(y'=\frac{1}{2}\times2 = 1\).

Answer:

\((-2,1)\)