Question

for the figure below, do a dilation centered at the origin with a scale factor of 3. then, give the endpoints for both the original figure and the final figure. endpoints of original figure: top: , bottom:

Explanation:

Step1: Identify original endpoints

From the grid, the original line segment has endpoints at \((3, 5)\) and \((7, 5)\) (assuming the grid coordinates: x - axis and y - axis with each grid unit as 1, and the points are at x = 3, y = 5 and x = 7, y = 5).

Step2: Apply dilation with scale factor 3

The formula for dilation centered at the origin \((0,0)\) is \((x,y)\to(3x,3y)\) (since scale factor \(k = 3\)).
For the first endpoint \((3,5)\):
New x - coordinate: \(3\times3=9\)
New y - coordinate: \(3\times5 = 15\)
So the new endpoint is \((9,15)\)
For the second endpoint \((7,5)\):
New x - coordinate: \(3\times7 = 21\)
New y - coordinate: \(3\times5=15\)
So the new endpoint is \((21,15)\)

Answer:

Original endpoints: \((3, 5)\) and \((7, 5)\); Final (dilated) endpoints: \((9, 15)\) and \((21, 15)\)