Question

for the figure below, do a dilation centered at the origin with a scale factor of 2. then, go points for both the original figure and the final figure. dilation 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 \((4,2)\) and the right - hand endpoint has coordinates \((6,8)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = 2\), the formula for dilation of a point \((x,y)\) is \((x',y')=(kx,ky)\).
For the point \((4,2)\):
\(x'=2\times4 = 8\), \(y'=2\times2=4\)
For the point \((6,8)\):
\(x'=2\times6 = 12\), \(y'=2\times8 = 16\)

Answer:

Endpoints of original figure:
Left: \((4,2)\)
Right: \((6,8)\)
Endpoints of final figure:
Left: \((8,4)\)
Right: \((12,16)\)