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 o**riginal 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.