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.

endpoints of original figure:

top: (, ) bottom: (, )

endpoints of final figure:

top: (, ) bottom: (, )

Explanation:

Step1: Identify original endpoints

From the graph, the top - point of the original figure has coordinates \((4,4)\) and the bottom - point has coordinates \((4,1)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = 4\), the formula for dilation is \((x,y)\to(kx,ky)\).
For the top - point \((x = 4,y = 4)\):
\((4\times4,4\times4)=(16,16)\)
For the bottom - point \((x = 4,y = 1)\):
\((4\times4,1\times4)=(16,4)\)

Answer:

Endpoints of original figure:
Top: \((4,4)\)
Bottom: \((4,1)\)
Endpoints of final figure:
Top: \((16,16)\)
Bottom: \((16,4)\)