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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

Please show your workTriangle ABC is rotated 180º using the origin as the center of rotation Which sequence of transformations will produce the same result a tr class=

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

Answer:

Option C is correct.

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

Step-by-step 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:

[tex](x,y) \rightarrow (x, -y)[/tex]

[tex]A(-4,-3) \rightarrow (-4, -(-3)) =(-4, 3) [/tex]

[tex]B(-5,-2) \rightarrow (-5, 2)[/tex]

[tex]C(-3, -2) \rightarrow (-3, 2)[/tex]

then,

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

[tex](x,y) \rightarrow (-x, y)[/tex]

[tex](-4,3) \rightarrow (4, 3)=A'[/tex]

[tex](-5,2) \rightarrow (5, 2)=B'[/tex]

[tex](-3,2) \rightarrow (3, 2)=C'[/tex]

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


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