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?
1. rotation, then translation
2. reflection, then rotation
3. translation, then rotation
4. only a rotation

Answer 1

Answer: 1. rotation, then translation.

Work: rotate ABC 90° counterclockwise about the origin, (x,y) -> (-y,x):
- A(-1,0) -> A' = (0,-1)
- B(3,-2) -> B' = (2,3)
- C(5,1) -> C' = (-1,5)

Then translate by (1,-3):
- A' + (1,-3) = (1,-4) = D
- B' + (1,-3) = (3,0) = E
- C' + (1,-3) = (0,2) = F

So a 90° CCW rotation followed by translation by (1,-3) maps triangle ABC to triangle DEF.