# Reflection of a Point in a Line Parallel to the y-axis

We will discuss here about reflection of a point in a line parallel to the y-axis.

Let P be a point whose coordinates are (x, y), AB be a line parallel the x-axis and the distance of AB from the y-axis be a. Let the image of P be P’ in the line AB

Clearly, P’ will be similarly situated on that side of AB which is opposite to P. So, the y-coordinates of P’ will be –x + 2a while the y-coordinate will be the same as that of P.

The image of the point (x, y) in the line parallel to the y-axis at a distance from the y-axis (i.e., x = a) is the point (-x + 2a, y), where a is taken positive if the line is on the positive side of the x-axis and a is taken negative if the line is on the negative side of the x-axis.

Examples:

(i) The image of the point (2, 4) in the line parallel to the y-axis at a distance 1 unit above the y-axis (i.e., x = 1) is (-2 + 2 × 1, 4), i.e., (0, 4)

(ii) The image of the point (-3, 5) in the line parallel to the y-axis at a distance 2 units below the x-axis (i.e., x = -2) is (3 + 2 × (-2), 5), i.e., (-1, 5)

Reflection