Question

Triangle XYZ is mapped onto triangle X′Y′Z′ by a dilation with a scale factor of 3 and center (2,1). What are the coordinates of triangle X′Y′Z′ when X(-3,2), Y(0,0), Z(2,1).

Don't forget that your ordered pairs need to be in parentheses and the coordinates separated by a comma!

X'=

Y'=

Z'=

30 points

Answer 1

Explanation:

To find the image of each point under the dilation, we need to apply the scale factor of 3 to the distances between the point and the center, and then add the coordinates of the center to get the new coordinates.

The center of dilation is (2,1), so we subtract 2 from the x-coordinates and 1 from the y-coordinates to get the distances from the center to each point:

X: (-3 - 2, 2 - 1) = (-5, 1)

Y: (0 - 2, 0 - 1) = (-2, -1)

Z: (2 - 2, 1 - 1) = (0, 0)

Next, we apply the scale factor of 3 to each distance:

X': (-5 × 3, 1 × 3) = (-15, 3)

Y': (-2 × 3, -1 × 3) = (-6, -3)

Z': (0 × 3, 0 × 3) = (0, 0)

Finally, we add the coordinates of the center (2,1) to each image:

X': (-15 + 2, 3 + 1) = (-13, 4)

Y': (-6 + 2, -3 + 1) = (-4, -2)

Z': (0 + 2, 0 + 1) = (2, 1)

Therefore, the coordinates of the image triangle X'Y'Z' are:

X' = (-13, 4)

Y' = (-4, -2)

Z' = (2, 1)