Question

Johnny reflects ∆ABC across the y axis and then again across the x axis. Hallie rotates ∆ABC 180 degrees clockwise about the origin. Sally says the resulting images will have the same coordinates. True or False?

Answer 1

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,

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

After that the it reflects along x-axis then,

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

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,

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

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.