# Reflection of a point

In this chapter we will learn reflection of a point along cartesian coordinates.

Let us first review the basics of reflection.

## What is Reflection ?

The mirror image of any object is called reflection.

The mirror image can be produced by entities like mirror, glass or water.

Some properties of reflection are;

(a) The mirror image is always flipped in orientation.

(b) The original object and image produced is equidistant from the central axis.

(c) The image has same size and dimension as original image.

## Reflection of Point

When a point is reflected in a mirror, we get;

(a) same point as an image

(b) the image is located equidistant from central axis as the original point.

For example, consider the point A in below image.

When point A is placed in front of mirror, we get reflected image which has same size & dimension of original point.

Note that the distance of reflected image to mirror is same as the original point distance to the same mirror but in opposite direction.

### Types of Point Reflection

There are three types of point reflection in geometry;

(a) Reflection of point along x axis
(b) Reflection of point along y axis
(c) Reflection of point along origin

We will understand each of the types one by one.

#### Reflection of point along x axis

Here the x axis of cartesian coordinate act as a mirror.

In this case when a point is placed in front of x axis we get the reflected image on the other side of the x axis at a same distance as original image.

In the above image;

⟹ Original Point is at (0, 2)

⟹ Red line is x axis which act as a mirror

⟹ Reflected Point is at (0, -2)

Note that the original and reflected point are equidistant from the x axis.

#### Reflection of Point along y axis

Here y axis act as an a mirror.

When a point is placed in front of y axis, we get the reflected image in opposite direction at same distance as original image from y axis.

For example;

Observe the above image;

⟹ (-2, 0) is the original point

⟹ Red line is x axis which act as a mirror

⟹ (2, 0) is the reflected image

Note that the reflected image is at opposite direction of original point and has same distance as length between original point and the mirror.

#### Reflection of point along Origin

In cartesian plane, when object is placed around origin, we get reflected image in opposite direction.

In this process the distance between reflected image & origin is same as the distance between original image & origin.

For example, consider the image below;

Note that;
⟹ (3, 2) is the location of original point
⟹ the origin (0 , 0) act as point of mirror
⟹ (-3, -2) is the mirror image

For your better understanding, given below is the mirror line through which reflection occurs.

Note that unlike reflection from x or y axis, the mirror line from origin changes as per the position of original point.

When the position change, the mirror line will also change.

For example, observe the below image.

Note that the reflected image lies at opposite direction of original image.

In this case, the mirror axis is shown by green line.

Conclusion
In reflection of point along origin, we get the reflected point at opposite direction of original image.

You cannot copy content of this page