# Reflection over the origin

In this chapter we will learn how to form a reflection of point over origin in a cartesian plane.

Let us first review the basics of reflection.

## What is Reflection ?

The mirror image of any object is known as reflection.

Reflected image can be produced by mirror, glass or water.

Every morning when you see yourself in the mirror, you see your reflected image.

The reflected image has same size and dimension but it is flipped in orientation.

## Reflection of point over origin

In this method the given object is reflected over the origin to produce image in completely opposite direction.

For example, consider the below image.

Here the original point is at (-3, 2).

After reflection, we get the mirror image at completely opposite direction at (3, -2)

Note that both the original and reflected image is equidistant from the origin.

Conclusion
After reflection over the origin, the mirror image is formed at opposite direction.

### Shortcut rule for reflection of point over origin

For a given point, the location of reflected image over origin can be found by changing the sign of both x & y coordinate of the original image.

Let us understand the rule with some examples.

For example;
The point (-3, -6) is reflected over origin. Find the location of reflected image.

Solution
To find the reflected image over origin, just change the sign of given x & y coordinates.

Hence, the location of mirror image is (3, 6)

Let us show the reflection in graphical image.

In the above image;
⟹ (-3, -6) is the original point
⟹ (3, 6) is the mirror image

Example 02
The point (2, 1) is reflected from origin. Find the location of reflected image.

Solution
To find the reflected image around origin, just change the sign of x & y coordinates.

Hence the reflected point is (-2, -1).

Representing the reflection in graphical form.

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