Map quadrilateral ABCD to quadrilateral A′B′C′D′ with a rotation of 180° about the origin followed by a translation 3 units left and 7 units up.

See Explanation

Step-by-step explanation:

Given

Shape: Quadrilateral ABCD

Transformations:

180 degrees rotation

3 units left

7 units up

Required

Determine A′B′C′D

The coordinates of ABCD is not given; So, I will solve generally.

Assume the coordinates of ABCD is (x,y)

When (x,y) is rotated 180 degrees, the new point is: (-x, -y)

Solving further:

Translation 3 units left

When a point (x,y) is translated b units left, the new point is (x - b, y).

So:

Translation 7 units up

When a point (x,y) is translated h units up, the new point is (x, y + b).

So:

Assume that the coordinates of A in ABCD before translation is (2,6).

i.e. A = (2,6)

The image A' will be: