Question

the figure below is dilated with the center of dilation at the origin and a scale factor of. what are the coordinates of the image of point b after this transformation?

Explanation:

Step1: Determine the coordinates of point B

From the graph, the coordinates of point B are \((4,-8)\).

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated with a center at the origin and a scale factor \(k\), the formula for the image of the point is \((kx,ky)\). Here \(k = \frac{1}{2}\), \(x = 4\), and \(y=-8\).
Substitute the values into the formula: \(x'=\frac{1}{2}\times4\), \(y'=\frac{1}{2}\times(-8)\).
Calculate \(x' = 2\) and \(y'=-4\).

Answer:

\((2,-4)\)