Question

for the figure below, do a dilation centered at the origin with a scale factor of 4. then, give the endpoints for both the original figure and the final figure.

Explanation:

Step1: Identify original endpoints

The original top - point is \((8,7)\) and the original bottom - point is \((8,1)\)

Step2: Apply dilation formula

For a dilation centered at the origin \((x,y)\to(kx,ky)\) with \(k = 4\).
For the top - point: \(x = 8,y=7,k = 4\), then \((8\times4,7\times4)=(32,28)\)
For the bottom - point: \(x = 8,y = 1,k = 4\), then \((8\times4,1\times4)=(32,4)\)

Answer:

Endpoints of original figure:
Top: \((8,7)\)
Bottom: \((8,1)\)
Endpoints of final figure:
Top: \((32,28)\)
Bottom: \((32,4)\)