We will first write an equation for the coordinates of the point P(x,y) reflected across the y-axis.
Reflection Across the y-axis
Let's find the coordinates of the point P(x,y) reflected across the y-axis.
R_(y-axis)(P(x,y)) = ?
We will draw a diagram to find the location of the reflected point P'. To do so, we will move along the line through P that is perpendicular to the line of reflection. Then, we stop when the distances of P and P' to the line of reflection are the same.
We see that the point P'(- x,y) is the image of P(x,y). Therefore, we can write the equation for the coordinates of the point P(x,y) reflected across the y-axis as follows.
R_(y-axis)(P(x,y)) = P'(- x,y)
Reflection Across the x-axis
We will now find the coordinates of a point P(x,y) reflected across the x-axis.
R_(x-axis)(P(x,y)) = ?
Let's draw a diagram to find the location of the reflected point. To do so, we will move along the line through P that is perpendicular to the line of reflection and then stop when the distances of P and P' to the line of reflection are the same.
We see that the point P'(x,- y) is the image of P(x,y). Therefore, we can write the equation for the coordinates of the point P(x,y) reflected across the x-axis as follows.
R_(x-axis)(P(x,y)) = P'(x,- y)
