Question

Parallelogram ABCD has vertex coordinates A(0, 1), B(1,3), (4,3), and D(3,1). It is translated 1 unit to the right and 3 units down and then rotated 180°clockwise around the origin. What are the coordinates of A?

Answer 1

A'(-1, 2)

Explanation:

Translation 1 right and 3 down is accomplished by the transformation ...

(x, y) ⇒ (x +1, y -3)

Rotation 180° is accomplished by ...

(x, y) ⇒ (-x, -y)

Then the composition of transformations gives ...

(x, y) ⇒ (-x -1, -y+3)

The transformed coordinates of A(0, 1) are ...

A(0, 1) ⇒ A'(-0 -1, -1 +3) = A'(-1, 2)