# Reflection of a Point in the y-axis

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

Reflection in the line x = 0 i.e., in the y-axis.

The line x = 0 means the y-axis.

Let P be a point whose coordinates are (x, y).

Let the image of P be P’ in the y-axis.

Clearly, P’ will be similarly situated on that side of OY which is opposite to P. So, the x-coordinates of P’ will be – x while its y-coordinates will remain same as that of P.

The image of the point (x, y) in the y-axis is the point (-x, y).

Symbolically, My (x, y) = (-x, y)

Rules to find the reflection of a point in y-axis:

(i) Change the sign of abscissa i.e. x-coordinate.

(ii) Retain the ordinate i.e., y-coordinate.

Therefore, when a point is reflected in the y-axis, the sign of its abscissa changes.

Examples:

(i) The image of the point (3, 4) in the y-axis is the point (-3, 4).

(ii) The image of the point (-3, -4) in the y-axis is the point (-(-3), -4) i.e., (3, -4).

(iii) The image of the point (0, 7) in the y-axis is the point (0, 7).

(iv) The image of the point (-6, 5) in the y-axis is the point (-(-6), 5) i.e., (6, 5).

(v) The reflection of the point (5, 0) in the y-axis = (-5, 0) i.e., My (5, 0) = (-5, 0)

Solved example to find the reflection of a point in the y-axis:

Find the points onto which the points (11, -8), (-6, -2) and (0, 4) are mapped when reflected in the y-axis.

Solution:

We know that a point (x, y) maps onto (-x, y) when reflected in the y-axis. So, (11, -8) maps onto (-11, -8); (-6, -2) maps onto (6, -2) and (0, 4) maps onto (0, 4).

Reflection