# Reflection of a Point in the Origin

We will discuss here how to find the reflection of a point in the origin.

Let M (a, b) be any point in the coordinate plane and O be the origin. Now join M and O, and produce it to the point M’ such that M’O = OM. Then the point M’ is the reflection of the point M in the origin. Thus, M’ is the image of M in the origin O. From the figure, we find that the coordinates of the point M’ are (-a, -b).

Thus, the reflection of the point M (a, b) in the origin is the point M’ (-a, -b)

Or

The image of the point (a, b) in the origin is the point (-a, -b).

Symbolically M $$_{o}$$ (a, b) = (-a, -b).

Rules to find the reflection of a point in the origin:

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

(ii) Change the sign of y-coordinate i.e. ordinate.

For example:

(i) Reflection of the point (5, 6) in the origin is the point (-5, -6) i.e. M $$_{o}$$ (5, 6) = (-5, -6)

(ii) Reflection of the point (7, -3) in the origin is the point (-7, 3) i.e. M $$_{o}$$ (7, -3) = (-7, 3)

Solved examples to find the reflection of a point in the origin:

Find the points onto which the following points are mapped on reflection in the origin.

(i) (4, 9)

(ii) (-1/4, 1/6)

(iii) (10, -15)

(iv) (-a, -b)

Solution:

We know that a point (x, y) is mapped onto the point (-x, -y) on reflection in the origin.

(i) (4, 9) maps onto (-4, -9)

(ii) (-1/4, 1/6) maps onto (1/4, -1/6)

(iii) (10, -15) maps onto (-10, 15)

(iv) (-x, -y) maps onto (x, y)

Reflection