Question

A rhombus has coordinates A(-6, 3), B(-4, 4), C(-2, 3), 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 ?

Answer 1

See below.

Explanation:

Firstly the counterclockwise rotation is (x, y) ---> (-y, x), so A(-6, 3) moves to (-3, -6).

Then the translation (-3, -6) ---> ( -3-3), -6) = (-6, -6) (3 units to the left).

Finally the second translation moves (-6, -6) to (-6, -6-2) = (-6, -8) = A' ( 2 units down).

The coordinates of B', C' and D' are calculated in exactly the same way.