Question

PLZ HELP

Figure PQRS is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure P′Q′R′S′:

A coordinate grid is labeled from negative 5 to 0 to 5 on both x and y axes at increments of 1. Figure PQRS has P at ordered pair negative 4, negative 2, Q at negative 2, negative 3, R at negative 3, negative 4, S at negative 4, negative 4. Figure P prime Q prime R prime S prime has P prime at ordered pair 4, 2, Q prime at 2, 3, R prime at 3, 4, S prime at 4, 4.

Which statement best compares the lengths of the sides of the two figures?

Length of PQ = Length of P′Q′
Length of PQ = Length of R′S′
Length of RS = Length of P′Q′
LENGTH of RS= length of Q' R

Answer 1

Length of PQ = Length of P′Q′

Answer 2

The correct option is 1.

Explanation:

From the figure it is clear that the vertices of figure PQRS are P(-4,-2), Q(-2,-3), R(-3,-4) and S(-4,-4).

The vertices of figure P'Q'R'S' are P'(4,2), Q'(2,3), R'(3,4) and S'(4,4).

The figure PQRS is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure P′Q′R′S′.

Rotation is a rigid transformation, it means the shape and size of the figure remains same. In other words, the preimage and image are similar figures.

`PQRS\cong P'Q'R'S'`

The corresponding parts of congruent figures are congruent.

`PQ\cong P'Q'`

`PQ=P'Q'` (Definition of congruence)

Since the length of PQ = Length of P′Q′. Therefore the correct option is 1.