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

Assume the left - hand endpoint of the original figure is $(x_1,y_1)$ and the right - hand endpoint is $(x_2,y_2)$. From the graph (assuming the left point is at $(8,6)$ and the right point is at $(10,6)$).

Step2: Apply dilation formula

The formula for dilation centered at the origin with a scale factor $k$ is $(x,y)\to(kx,ky)$. Here $k = 2$. For the left - hand endpoint $(x_1,y_1)=(8,6)$, the new point is $(2\times8,2\times6)=(16,12)$. For the right - hand endpoint $(x_2,y_2)=(10,6)$, the new point is $(2\times10,2\times6)=(20,12)$.

Answer:

Endpoints of original figure:
Left: $(8,6)$
Right: $(10,6)$
Endpoints of final figure:
Left: $(16,12)$
Right: $(20,12)$