Representing Transformations
Reflecting about the Line y=x
Reflecting about the Line y=x
The arbitrary point P(x,y) goes to P'(y,x) when reflected across the line y=x. This means that the point transforms to another point with the first point's y value as the x value and the x value as the y value. It can also be represented by multiplying the (x,y) coordinate in the form of a 2x1 matrix by the matrix below to get the new point.
0 1
1 0
Reflecting about y=0 or x=0
Reflecting about y=0 or x=0
The arbitrary point P(x,y) goes to P'(-x,y) when reflected across the line y=0(orange). This reflections simply changes the x value to being equal but on the opposite side of the x axis. It can also be represented by multiplying the (x,y) coordinate in the form of a 2x1 matrix by the matrix below to get the new point.
-1 0
0 1
The arbitrary point P(x,y) goes to P'(x,-y) when reflected across the line x=0(purple). Similarly to reflecting over the x axis, reflecting over the y axis changes the y value to being equal but to the opposite side of the y axis. It can also be represented by multiplying the (x,y) coordinate in the form of a 2x1 matrix by the matrix below to get the new point.
1 0
0 -1