Question

Which transformations can be used to carry ABCD onto itself? The point of

rotation is (3,2). Check all that apply.

Answer 1

B and D

Explanation:

Answer 2

The correct option is B.

Explanation:

From the given figure it is clear that the A(1,1), B(5,1), C(5,3) and (1,3).

The point of rotation is (3,2).

If a figure rotated 180° about a point (a,b) then

`(x,y)\rightarrow (2a-x,2b-y)`

The figure rotated 180° about the point (3,2) then

`(x,y)\rightarrow (2(3)-x,2(2)-y)`

`(x,y)\rightarrow (6-x,4-y)`

The vertices of image are

`A(1,1)\rightarrow A'(5,3)`

`B(5,1)\rightarrow B'(1,3)`

`C(5,3)\rightarrow C'(1,1)`

`D(1,3)\rightarrow D'(5,1)`

The vertices of image are same as vertices of preimage. So, after rotation of 180° about the point (3,2) the figure ABCD onto itself.

Therefore the correct option is B.