Question

The coordinate plane shows the locations of triangle 1 and triangle 2.

The triangle 1 has vertices at (-4, 2), (-5, 5), and (-1, 4). The tringle 2 has vertices at (2, -4), (5, -5), and (4, -1).

Jessica made the following statement.

Triangle 2 is the result of a specific rigid motion: a rotation of triangle 1 about the origin. The result is two triangles that are similar to one another but not congruent.
Which of these best describes Jessica's statement?

A.
She made an incorrect statement. The two triangles are not similar because the angles for triangle 2 are not the same as for triangle 1.

B.
She made two errors. The rigid motion is a reflection not a rotation and the two triangles are both similar and congruent.

C.
She made a correct statement.

D.
She called the transformation a rigid motion, when actually it is not. In addition, she describes triangle 2 as being a rotation, when it is the result of a reflection. Also, the two triangles are both similar and congruent.

Answer 1

B

Reflection across the line y = x maps each vertex (x, y) of triangle 1 to (y, x), giving (2, -4), (5, -5), (4, -1). So the transformation is a reflection (a rigid motion), not a rotation, and rigid motions produce congruent (as well as similar) figures. Jessica was wrong about the rotation and about them not being congruent.