Question

Please show your work.

Triangle ABC is rotated 180º using the origin as the center of rotation.
Which sequence of transformations will produce the same result?
a translation up 4 and then a reflection over the y-axis
a translation up 4 and then a translation right 6
a reflection over the x-axis and then a reflection over the y-axis
a translation right 6 and then a reflection over the x-axis

Answer 1

The answer would be a reflection over the x-axis and then a reflection over the y-axis

Answer 2

Option C is correct.

A reflection over the x-axis and then a reflection over the y-axis

Explanation:

From the given figure:

The coordinates of ABC are:

A(-4, -3), B(-5, -2) and C(-3, -2).

and the coordinate of A'B'C' are:

A'(4, 3), B'(5, 2) and C(3, 2)

The rule of reflection over x-axis is given by:

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

`A(-4,-3) \rightarrow (-4, -(-3)) =(-4, 3)`

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

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

then,

The rule of reflection over y-axis is given by:

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

`(-4,3) \rightarrow (4, 3)=A'`

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

`(-3,2) \rightarrow (3, 2)=C'`

Therefore, the triangle ABC is rotated 180 degree using the origin as the center of rotation is: A reflection over the x-axis and then a reflection over the y-axis