# 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

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Estimating Sum and Difference | Reasonable Estimate | Procedure | Math

May 22, 24 06:21 PM

The procedure of estimating sum and difference are in the following examples. Example 1: Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

2. ### Round off to Nearest 1000 |Rounding Numbers to Nearest Thousand| Rules

May 22, 24 06:14 PM

While rounding off to the nearest thousand, if the digit in the hundreds place is between 0 – 4 i.e., < 5, then the hundreds place is replaced by ‘0’. If the digit in the hundreds place is = to or > 5…

3. ### Round off to Nearest 100 | Rounding Numbers To Nearest Hundred | Rules

May 22, 24 05:17 PM

While rounding off to the nearest hundred, if the digit in the tens place is between 0 – 4 i.e. < 5, then the tens place is replaced by ‘0’. If the digit in the units place is equal to or >5, then the…

4. ### Round off to Nearest 10 |How To Round off to Nearest 10?|Rounding Rule

May 22, 24 03:49 PM

Round off to nearest 10 is discussed here. Rounding can be done for every place-value of number. To round off a number to the nearest tens, we round off to the nearest multiple of ten. A large number…