Question

Identify the rotation rule on a coordinate plane that verifies that triangle A(2,-1), B(4,1), C(3,3) and triangle A'(1,2), B'(-1,4), C'(-3,3) are congruent when rotated 90°.

Answer 1

The rotation rule that verifies the congruence of the triangles is:

(x, y) → (-y, x)

Applying this rule to triangle A(2,-1), we get:

A'(-1, 2)

Applying the rule to triangle B(4, 1), we get:

B'(-1, 4)

Applying the rule to triangle C(3, 3), we get:

C'(-3, 3)

Therefore, triangle A'(-1, 2), B'(-1, 4), and C'(-3, 3) are congruent to triangle A(2,-1), B(4,1), and C(3,3) when rotated 90°.