Question

figure a was rotated 135° counterclockwise about the origin to form figure a. what is the perimeter of figure a? enter the answer in the box. units

Explanation:

Step1: Determine side lengths of Figure A

For Figure A (a rectangle), length \( l = 6 - 2 = 4 \) (difference in x - coordinates), width \( w = 4 - 1 = 3 \) (difference in y - coordinates).

Step2: Recall rotation property

Rotation is a rigid transformation, so the side lengths of Figure A' are the same as Figure A.

Step3: Calculate perimeter of Figure A'

Perimeter of a rectangle is \( P = 2(l + w) \). Substituting \( l = 4 \) and \( w = 3 \), we get \( P = 2(4 + 3)=2\times7 = 14 \).

Answer:

14