Question

A rectangle with vertices A(-3, 1), B(1, 3), C(2, 1), and D(-2, -1) is rotated 90° clockwise about the origin and then dilated by a factor of 3 with the origin as the center of dilation to obtain rectangle A′B′C′D′. Which statement about the transformed rectangle A′B′C′D′ is true?

A.
The function f(x, y) = (-3y, 3x) models the transformation to obtain rectangle A′B′C′D′, and vertex C′ lies in the first quadrant.
B.
The function f(x, y) = (-3y, 3x) models the transformation to obtain rectangle A′B′C′D′, and vertex D′ lies in the second quadrant.
C.
The function f(x, y) = (3y, -3x) models the transformation to obtain rectangle A′B′C′D′, and vertex B′ lies in the fourth quadrant.
D.
The function f(x, y) = (3y, -3x) models the transformation to obtain rectangle A′B′C′D′, and vertex A′ lies in the third quadrant.

Answer 1

A rotation clockwise will transform a point
\[(x,y)\]
into
\[(y,-x)\]
and a dilation by a factor k will transform into
\[(ky, -kx)\]