Question

if a line segment from (2,2) to (4,4) is dilated by a scale factor of 3 with the origin as the center, what are the new coordinates of the endpoints?

a. (3, 3) to (12, 12)

b. (6, 6) to (12, 12)

c. (5, 5) to (7, 7)

d. (6, 6) to (9, 9)

Explanation:

Step1: Recall dilation formula

When dilating a point \((x,y)\) with the origin as the center and scale factor \(k\), the new coordinates are \((kx, ky)\).

Step2: Dilate the first endpoint \((2,2)\)

For the point \((2,2)\) and scale factor \(3\), we calculate the new \(x\)-coordinate as \(3\times2 = 6\) and the new \(y\)-coordinate as \(3\times2=6\). So the new coordinate is \((6,6)\).

Step3: Dilate the second endpoint \((4,4)\)

For the point \((4,4)\) and scale factor \(3\), we calculate the new \(x\)-coordinate as \(3\times4 = 12\) and the new \(y\)-coordinate as \(3\times4 = 12\). So the new coordinate is \((12,12)\).

Answer:

b. \((6,6)\) to \((12,12)\)