# Reflection in Lines Parallel to Axes

We will discuss here how to solve the problems on reflection in lines parallel to axes (x = a or y = b).

The coordinates of the points P and Q are (5, -4) and (-2, 10) respectively.

(i) Find the point P’ and Q’onto which the points P and Q map on reflection in the line AB which is parallel to the x-axis and is at a distance 3 on the positive side of the y-axis.

(ii) Find the point P” and Q”onto which the points P and Q map on reflection in the line CD which is parallel to the y-axis and is at a distance 3 on the negative side of the x-axis.

Solution:

(i) We know that the image of the point (x, y) in the line parallel to the x-axis and at a distance a from the x-axis in the positive side of the y-axis is the point (x, -y + 2a). Here, a = 3 and the coordinates of P are (5, -4). So, the coordinates of P’ are (5, -(-4) + 2 × 3), i.e., (5, 10). The coordinates of Q are (-2, 10). So the coordinates of Q’ are (-2, -10 + 2 × 3), i.e., (-2, -4).

(ii) We know that the image of the point (x, y) in the line parallel to the y-axis and at a distance a from the y-axis in the negative side of the x-axis is the point (-x + 2a, y). Here, the coordinates of P are (5, -4) and a = -3. So, the coordinates of P” are (-5 + 2 (-3), -4), i.e., (-11, -4). The coordinates of Q are (-2, 10). So the coordinates of Q” are (2 + 2(-3), 10), i.e., (-4, 10).