# Reflection in math

In this chapter we will learn basic concept of reflection and its properties.

## Reflection geometry definition ?

Reflection is basically a mirror image of any given body.

In reflection we get a flipped image which is identical in size and design.

Using the above reflected image, we will understand the below properties;

(a) Reflection can be produced by mirror, glass, water etc. Even if you stand in front of a lake, you will get your reflection in the water.

(b) The image produced by reflection is flipped in orientation.

In the above example, notice how the main object ” C ” gets flipped in the reflection.

(c) the reflected image is identical in size & shape.

(d) Original image and reflected image are equidistant from central axis but in opposite direction.

In the above example, the original and reflected image is located equidistant from the central axis O.

(e) Reflected image are also known as mirror image.

When you stand in front of the mirror, you see your reflected image produced inside the mirror.

I hope you understood the above properties. Let us look at some examples for further understanding.

## Type of Reflection

We can have different type of reflection depending on the direction of mirror line.

In general there are three types of reflection.

(a) Horizontal reflection
(b) Vertical reflection
(c) Diaginal reflection

Let us discuss each of them with examples.

### Horizontal Reflection

When the mirror axis is placed horizontally we get horizontal reflection.

For example;

Given above is the horizontal placed mirror axis O at the center.

Here the original image ” M ” is flipped horizontally to produce the reflected image.

Notice that both the original and reflected image are equidistant from central line O.

### Vertical Reflection

When the mirror axis is placed vertically we get the vertical reflection.

In the above example, the mirror axis O is placed horizontally.

Here the original image ” P ” is flipped horizontally to produce the reflected image.

### Diagonal Reflection

When the central mirror axis is tilted, we get the diagonal reflection.

Given above is the mirror axis O which is tilted in direction.

Notice the original and mirror image produced by the diagonal mirror axis.

Also observe that both the images are located equidistance from the center axis O.

## How to draw mirror image ?

You can easily draw reflected image by following the below steps;

(a) Locate the vertex point of the given figure.

(b) Now draw the perpendicular line to the mirror axis O and measure the length.

(c) Extend the perpendicular line to other side of mirror axis to the same measured original length.

(d) Connect all the points and you will get the reflected image.

Note:
This method will only work for simplistic geometrical diagram.

Let us understand the above process with the help of examples;

Example 01
Draw the vertical reflected image of below triangle.

Solution
To draw the reflected image, follow the below steps.

(a) Locate & mark the vertex point of given figure.

(b) Draw perpendicular line to mirror axis and measure the length.

(c) Now extend the line to same length to other side of mirror and mark the points.

(d) Join all the points and you will get reflected image of the triangle.

The reflected image has same side length & angle measurement as the original triangle.

Also, both original & reflected images are located at equal distance from the Mirror axis O.

Example 02
Draw the horizontal reflected image of below triangle.

Solution
For horizontal reflected image, we will use horizontal mirror.

(a) Locate and mark the vertex point of given figure.

(b) Draw perpendicular line to mirror axis and measure the length.

(c) Extend the vertical line to the same length to other side of the mirror axis and mark the points.

(d) Join all the points

Hence, we got the horizontal reflection of given triangle.

Example 03
Draw vertical reflection of given image.

Solution
For the vertical reflection we will use the vertical mirror axis.

(a) Locate and mark the vertex point of the given figure.

(b) Draw perpendicular line to Mirror axis from the vertex.

(c) Extend the line to other side of Mirror Axis to the same length and then mark the points.

(d) Join all the points.

After joining all the points we will get the mirror image.