Question

for the figure below, do a dilation centered at the origin with a scale factor of $\frac{1}{4}$. 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: Find original endpoints

From the graph, the left - hand endpoint (the upper point) has coordinates \((8,16)\) and the right - hand endpoint (the lower point) has coordinates \((12,0)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k=\frac{1}{4}\), if a point has coordinates \((x,y)\), the coordinates of the dilated point \((x',y')\) are given by \(x' = kx\) and \(y'=ky\).
For the point \((8,16)\):
\(x'=\frac{1}{4}\times8 = 2\), \(y'=\frac{1}{4}\times16 = 4\)
For the point \((12,0)\):
\(x'=\frac{1}{4}\times12 = 3\), \(y'=\frac{1}{4}\times0 = 0\)

Answer:

Endpoints of original figure:
Left: \((8,16)\)
Right: \((12,0)\)
Endpoints of final figure:
Left: \((2,4)\)
Right: \((3,0)\)