A rhombus has coordinates A (-6, 3), B (-4, 4), C (-2, 3), and D (-4, 2). What are the coordinates of rhombus A′B′C′D′ after a 90° counterclockwise rotation about the origin followed by a translation 3 units to the left and 2 units down?

We are given that the coordinates of the vertices of the rhombus are:

A (-6, 3)

B (-4, 4)

C (-2, 3)

D (-4, 2)

To solve this problem, we must plot this on a graphing paper or graphing calculator to clearly see the movement of the graph. If we transform this by doing a counterclockwise rotation, then the result would be:

A (-6, - 3)

B (-4, - 4)

C (-2, - 3)

D (-4, - 2)

And the final transformation is translation by 3 units left and 2 units down. This can still be clearly solved by actually graphing the plot. The result of this transformation would be:

A′ (6, - 8)

B′ (7, - 6)

C′ (6, - 4)

D′ (5, - 6)