Question

Triangle A"B"C" is the image of triangle ABC after a sequence of transformations. Which sequence of tranformations could have been applied?

Answer 1

The answer is A
ABC is translated 1 unite to the right then rotated 180 Clockwise about the original

Answer 2

The correct option is C.

Explanation:

From the given figure it is clear that the vertices of figure ABC are A(-2,2), B(0,5) and C(2,2).

The vertices of figure A''B''C'' are A''(0,-2), B''(-2,-5) and C''(-4,-2).

If a figure translated two units right then

`(x,y)\rightarrow (x+2,y)`

`A(-2,2)\rightarrow A'(0,2)`

`B(0,5)\rightarrow B'(2,5)`

`C(2,2)\rightarrow C'(4,2)`

After that the figure rotated 180° clockwise about the origin.

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

`A'(0,2)\rightarrow A''(0,-2)`

`B'(2,5)\rightarrow B''(-2,-5)`

`C'(4,2)\rightarrow C''(-4,-2)`

Therefore ΔABC translated 2 units right, then rotated 180° clockwise about the origin.

Hence the correct option is C.