Question

Which of these statements is true about the two trapezoids graphed below?

The coordinate plane showing a trapezoid in the second quadrant with its vertices at point (-1, 2), point (-5, 2), point (-4, 5) and point (-2, 5) and another trapezoid in the fourth quadrant with its vertices at point (2, -2), point (4, -2), point (5, -5) and point (1, -5).
A.
They are congruent, because one can be obtained by translating the other 6 units to the right and 7 units down.

B.
They are congruent, because one can be obtained by translating the other 7 units to the right and 6 units down.

C.
They are not congruent, because one can be obtained by translating the other 6 units to the right and 7 units down.

D.
They are not congruent, because one can be obtained by translating the other 7 units to the right and 6 units down.

Answer 1

A. They are congruent, because translating each vertex of the first trapezoid by (+6, −7) yields the corresponding vertex of the second:
(-1,2)+(6,−7)=(5,−5), (-5,2)+(6,−7)=(1,−5), (-4,5)+(6,−7)=(2,−2), (-2,5)+(6,−7)=(4,−2).