Question

for the figure below, do a dilation centered at the origin with a scale factor of 3. 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 coordinates \((1,5)\) and the right - hand endpoint has coordinates \((4,5)\).

Step2: Apply dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = 3\).
For the left - hand endpoint \((1,5)\):
\(x'=3\times1=3\), \(y'=3\times5 = 15\), so the new coordinates are \((3,15)\)
For the right - hand endpoint \((4,5)\):
\(x'=3\times4=12\), \(y'=3\times5=15\), so the new coordinates are \((12,15)\)

Answer:

Endpoints of original figure:
Left: \((1,5)\)
Right: \((4,5)\)
Endpoints of final figure:
Left: \((3,15)\)
Right: \((12,15)\)