Question

What rotation was applied to triangle DEF to create triangle D'E'F'?

d=(-1, 6)
e=(1, 3)
f=(6, 3)
d'=(1, -6)
e'=(-1, -3)
f'=(-6, -3)

Possible answers:
90° clockwise
180°
None of the above
90° counterclockwise

Answer 1

2. 180°

Explanation:

We are given the co-ordinates of ΔDEF as D(-1,6), E(1,3) and F(6,3).

Now, after rotation the co-ordinates of the new triangle D'E'F' are D'(1,-6), E'(-1,-3) and F'(-6,-3).

As we see that, the co-ordinates of triangle DEF are multiplied by negative sign to obtain the co-ordinates of triangle D'E'F'.

This means that, the triangle DEF is rotated 180° to form triangle D'E'F' because rotating 180 changes (x,y) to (-x,-y).

Hence, the rotation applied is 180° to ΔDEF.

Answer 2

A 180 degree rotation was applied. You can tell because both numbers in each ordered pair are reversed (positive to negative and negative to positive).