Mathematics: Which transformations can be used to carry abcd onto itself? the point of rotation is (3,2). check all that apply.

Point ‘N’ would be a reflection across the Y-Axis...

Which transformations can be used to carry abcd

madiiiiiii69

15.03.2022

The correct option is B.

Step-by-step 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.

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