Answer: The sally's conclusion is true and the both image have different coordinates.
Explanation:
It is given that johny reflects ∆ABC across the y axis and then again across the x axis.
Let the coordinate of A is (x,y) and it reflects along y-axis then,
[tex](x,y)\rightarrow(-x,y)[/tex]
After that the it reflects along x-axis then,
[tex](-x,y)\rightarrow(-x,-y)[/tex]
So, if the coordinate of A is (x,y) and Johnny reflects ∆ABC across the y axis and then again across the x axis, then A'(-x,-y).
It is given that Hallie rotates ∆ABC 180 degrees clockwise about the origin.
Let the coordinate of A is (x,y) and it rotates 180 degrees clockwise about the origin then,
[tex](x,y)\rightarrow(-x,-y)[/tex]
So, if the coordinate of A is (x,y) and Hallie rotates ∆ABC 180 degrees clockwise about the origin, then A'(-x,-y).
It is also represent in the figure with the help of a random triangle.
In both process we get the same images. Therefore, the sally's conclusion is true.
