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 the original endpoints

From the graph, the original left - hand endpoint has coordinates \((2,4)\) and the original right - hand endpoint has coordinates \((10,6)\)

Step2: Apply the dilation formula

For a dilation centered at the origin with a scale factor \(k = 2\), the formula for dilation is \((x,y)\to(kx,ky)\)

• For the point \((2,4)\):
• \(x = 2\), \(y = 4\), \(k = 2\)
• \(kx=2\times2 = 4\), \(ky = 2\times4=8\)
• For the point \((10,6)\):
• \(x = 10\), \(y = 6\), \(k = 2\)
• \(kx=2\times10 = 20\), \(ky=2\times6 = 12\)

Answer:

Endpoints of original figure: Left: \((2,4)\), Right: \((10,6)\)
Endpoints of final figure: Left: \((4,8)\), Right: \((20,12)\)