Question

Triangle with vertices X(0,5), Y(5,10), Z(15,-5); Dilation with a scale factor of 2/5. What is the image of point Z after the dilation?

A) Z'(6, -2)
B) Z'(4, -3)
C) Z'(9, -4)
D) Z'(3, -5)

Answer 1

A) Z'(6, -2)

To find the image of point Z after a dilation with a scale factor of 2/5, multiply both the x and y coordinates by 2/5. The image of point Z is Z'(6, -2), making the correct answer A) Z'(6, -2).

Step-by-step explanation:

The question involves the concept of dilation in geometry, which is a transformation that produces an image that is the same shape as the original, but is a different size. To determine the image of point Z after a dilation with a scale factor of 2/5, you must multiply the coordinates of Z by the scale factor. Thus, the new coordinates Z' would be obtained by multiplying the x-coordinate (15) and the y-coordinate (-5) of Z by 2/5.

Z'(x', y') = (15 * 2/5, -5 * 2/5) = (6, -2)
Therefore, the correct answer is A) Z'(6, -2).