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 b after this transformation?

Explanation:

Step1: Find the original coordinates of point B

From the graph, the coordinates of point B are \((4,-6)\).

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated with a center at the origin and a scale factor \(k\), the new coordinates \((x',y')\) are given by \(x' = kx\) and \(y'=ky\). Here \(k = \frac{1}{2}\), \(x = 4\), \(y=-6\).
So \(x'=\frac{1}{2}\times4\) and \(y'=\frac{1}{2}\times(-6)\)
\(x' = 2\), \(y'=-3\)

Answer:

\((2,-3)\)