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 has \(x = 4\) and \(y = 6\), so it is \((4,6)\). The right - hand endpoint of the original figure has \(x = 8\) and \(y = 6\), so it is \((8,6)\).

Step2: Apply dilation formula

The formula for dilation centered at the origin is \((x,y)\to(kx,ky)\), where \(k=\frac{1}{2}\).
For the left - hand endpoint \((4,6)\):
\(x'=\frac{1}{2}\times4 = 2\), \(y'=\frac{1}{2}\times6 = 3\). So the new left - hand endpoint is \((2,3)\).
For the right - hand endpoint \((8,6)\):
\(x'=\frac{1}{2}\times8 = 4\), \(y'=\frac{1}{2}\times6 = 3\). So the new right - hand endpoint is \((4,3)\).

Answer:

Endpoints of original figure:
Left: \((4,6)\)
Right: \((8,6)\)
Endpoints of final figure:
Left: \((2,3)\)
Right: \((4,3)\)