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 w after this transformation?

Explanation:

Step1: Find the coordinates of point W

From the graph, the coordinates of point W are \((1,-8)\).

Step2: Apply the dilation formula

When a point \((x,y)\) is dilated with a scale factor \(k\) and center of dilation at the origin \((0,0)\), the formula for the image of the point is \((kx,ky)\). Here \(k = \frac{1}{2}\), \(x = 1\), \(y=-8\).
So, the \(x\) - coordinate of the image is \(k\times x=\frac{1}{2}\times1=\frac{1}{2}\) and the \(y\) - coordinate of the image is \(k\times y=\frac{1}{2}\times(-8)= - 4\)

Answer:

\((\frac{1}{2},-4)\)