MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

Answer:The correct option is 1.Step-by-step 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.[tex]PQRS\cong P'Q'R'S'[/tex]The corresponding parts of congruent figures are congruent.[tex]PQ\cong P'Q'[/tex][tex]PQ=P'Q'[/tex] (Definition of congruence)Since the length of PQ = Length of P′Q′. Therefore the correct option is 1.