Figure abcd is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure a′b′c′d′:
a coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. figure abcd has a at ordered pair negative 4, negative 2, b at negative 2, negative 3, c at negative 3, negative 4, d at negative 4, negative 4. figure a prime b prime c prime d prime has a prime at ordered pair 4, 2, a prime at 2, 3, c prime at 3, 4, d prime at 4, 4.
which statement best compares the lengths of the sides of the two figures?
length of ab = length of c′d′
length of cd = length of a′b′
length of cd = length of b′c′
length of ab = length of a′b′

Length of AB = Length of A′B′

Step-by-step explanation:

Given : Figure ABCD is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure A′B′C′D′.

We know that a rotation is a rigid motion which does not changes shape and size of the figure.

It means the corresponding side lengths are equal.

Thus , if  Figure ABCD is rotated to form A′B′C′D′, then the corresponding sides of both of them are equal.

i.e. Length of AB = Length of A′B′

Length of BC = Length of B′C′

Length of CD = Length of C′D′

Length of DA = Length of D′A′

Hence, the statement best compares the lengths of the sides of the two figures :  Length of AB = Length of A′B′

were is the equation