Question

What set of transformations is performed on triangle abc to form triangle a'b'c'

Answer 1

Reflection over x-axis and Translation

Answer 2

The correct option is C.

Explanation:

From the given graph it is clear that the vertices of triangle ABC are A(4,-2), B(3,-2) and C(3,-5).

The vertices of triangle A'B'C' are A'(1,2), B'(2,2) and C'(2,5).

If a figure translated 5 units left, then

`(x,y)\rightarrow (x-5,y)`

The vertices of triangle after translation are

`A(4,-2)\rightarrow A_1(-1,-2)`

`B(3,-2)\rightarrow B_1(-2,-2)`

`C(3,-5)\rightarrow C_1(-2,-5)`

If a figure rotated 180° counterclockwise about the origin then

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

The vertices of triangle after rotation are

`A_1(-1,-2)\rightarrow A'(1,2)`

`B_1(-2,-2)\rightarrow B'(2,2)`

`C_1(-2,-5)\rightarrow C'(2,5)`

The set transformation is " A translation 5 units to the left followed by a 180° counterclockwise about the origin".

Therefore the correct option is C.