Question

for the figure below, do a dilation centered at the origin with a scale factor of 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: Identify original endpoints

From the graph, the original endpoints are \((4,4)\) and \((10,6)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = 2\), the formula is \((x,y)\to(kx,ky)\).
For \((4,4)\): \((2\times4,2\times4)=(8,8)\)
For \((10,6)\): \((2\times10,2\times6)=(20,12)\)

Answer:

Endpoints of original figure: \((4,4)\), \((10,6)\)
Endpoints of final figure: \((8,8)\), \((20,12)\)