Marisa says that reflecting a point across the x axis and then reflecting its image across the y-axis will produce the same final image as just reflecting the original point across the line y equals x is this true?
not in any way.
reflections
in x-axis: (x,y) -> (x,-y)
in y-axis: (x,y) -> (-x,y)
so, together: (x,y) -> (x,-y) -> (-x,-y)
in y=x: (x,y) -> (y,x)
so, can you find the single reflection that is equivalent?
No my teacher didn't teach us this just gave it to us for homework
To determine if Marisa's statement is true, we can visually analyze the transformations involved. Let's consider a point P with coordinates (x, y).
1. Reflecting the point across the x-axis:
When we reflect a point across the x-axis, we keep the y-coordinate the same, but change the sign of the x-coordinate. So, the new coordinates are (-x, y).
2. Reflecting the image across the y-axis:
When we reflect a point across the y-axis, we keep the x-coordinate the same, but change the sign of the y-coordinate. So, the new coordinates are (-x, -y).
Now, let's examine what happens when we reflect the original point across the line y = x:
3. Reflecting the point across the line y = x:
To reflect a point across y = x, we interchange the x and y coordinates. So, the new coordinates are (y, x).
Comparing the results from step 2 and step 3, we can see that they are not the same in general. In other words, reflecting a point across the x-axis and then reflecting its image across the y-axis does not produce the same final image as reflecting the original point across the line y = x.
Therefore, Marisa's statement is not true.