Question

The rule T1, -4 CompositionRO, 180°(x, y) is applied to rectangle KLMN.

On a coordinate plane, 5 rectangles are shown. Rectangle K L M N has points (3, negative 4), (3, negative 1), (5, negative 1), (5, negative 4). Rectangle 1 has points (negative 4, 6), (negative 4, 4), (negative 1, 4), (negative 1, 6). Rectangle 2 has points (0, 0), (negative 2, 0), (negative 2, 3), (0, 3). Rectangle 3 has points (negative 2, 0), (negative 4, 0), (negative 2, negative 3), (negative (4, negative 3). Rectangle 4 has points (1, 0), (4, 0), (1, 2), (4, 2).
Which rectangle shows the final image?

1
2
3
4

Answer 1

3

Rotation 180° about the origin sends (x,y) to (-x,-y). Then T1,-4 adds (1,-4). For the vertices:

- (3,-4) -> (-3,4) -> (-2,0)
- (3,-1) -> (-3,1) -> (-2,-3)
- (5,-1) -> (-5,1) -> (-4,-3)
- (5,-4) -> (-5,4) -> (-4,0)

These match rectangle 3.