Question

for the figure below, do a dilation centered at the origin with a scale factor of $\frac{1}{2}$. then, give the endpoints for both the original figure and the final figure. endpoints of original figure: left: ( , ) right: ( , ) endpoints of final figure: left: ( , ) right: ( , )

Explanation:

Step1: Find original endpoints

From the graph, the left - hand endpoint of the original figure is \((4,2)\) and the right - hand endpoint is \((8,8)\).

Step2: Apply dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = \frac{1}{2}\).
For the point \((4,2)\):
\(x'=\frac{1}{2}\times4 = 2\), \(y'=\frac{1}{2}\times2=1\)
For the point \((8,8)\):
\(x'=\frac{1}{2}\times8 = 4\), \(y'=\frac{1}{2}\times8 = 4\)

Answer:

Endpoints of original figure:
Left: \((4,2)\)
Right: \((8,8)\)
Endpoints of final figure:
Left: \((2,1)\)
Right: \((4,4)\)