Question

A rhombus with vertices P(2, 8), Q(3, 11), R(4, 8), and S(3, 5) is rotated 90° counterclockwise about the origin and then dilated by a factor of 2 with the origin as the center of dilation to obtain rhombus P′Q′R′S′. Which statement about the transformed rhombus P′Q′R′S′ is true? The function f(x, y) = (2y, -2x) models the transformation to obtain rhombus P′Q′R′S′, which lies in the second quadrant. The function f(x, y) = (-2y, 2x) models the transformation to obtain rhombus P′Q′R′S′, which lies in the fourth quadrant. The function f(x, y) = (-2y, 2x) models the transformation to obtain rhombus P′Q′R′S′, which lies in the second quadrant. The function f(x, y) = (2y, -2x) models the transformation to obtain rhombus P′Q′R′S′, which lies in the fourth quadrant.

Answer 1

The general rule for 90° degree counterclockwise rotation for a point (x,y) is:
(x,y)⇒(-y,x)
given that the image above is dilated by a scale factor of two, the final image will be:
2(-y,x)⇒(-2y,2x)
The new point lies in Quadrant IV

Thus the true statement about rhombus PQRS after undergoing 90° counter clockwise rotation followed by dilation of scale factor 2 is:

The function f(x, y) = (-2y, 2x) models the transformation to obtain rhombus P′Q′R′S′, which lies in the fourth quadrant, that is: IV Quadrant