Question

Triangle ABC= (-1, 0), (3, -2), (5, 1)
Triangle DEF= (1, -4), (3, 0), (0, 2)
How would you describe the transformations needed to show congruence between triangle ABC and triangle DEF? (Choose only one.)
rotation, then translation
reflection, then rotation
translation, then rotation
only a rotation

Answer 1

rotation, then translation

Explain: Rotate triangle ABC 90° counterclockwise about the origin: A(-1,0) -> (0,-1), B(3,-2) -> (2,3), C(5,1) -> (-1,5). Then translate by (1,-3): (0,-1)+(1,-3)=(1,-4)=D, (2,3)+(1,-3)=(3,0)=E, (-1,5)+(1,-3)=(0,2)=F.