Question

A rhombus TEMPhas 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

• A'(-6, -8)
• B'(-7, -6)
• C'(-6, -4)
• D'(-5, -6)

Explanation:

A 90° CCW rotation makes the transformation ...

(x, y) ⇒ (-y, x)

A translation 3 left and 2 down makes the transformation ...

(x, y) ⇒ (x -3, y-2)

The two transformations together are ...

(x, y) ⇒ (-y-3, x -2)

Then the given points are transformed to ...

A'(-6, -8)

B'(-7, -6)

C'(-6, -4)

D'(-5, -6)