# Reflection over x axis

In this chapter we will learn the concept of reflection across the x axis with solved examples.

Let us first review the basics of reflection.

## What is Reflection ?

The formation of mirror image of any body is called reflection.

The reflected image has following property;

(a) it is flipped in orientation
(b) it has same size and dimensions
(c) it is located in opposite direction of original object

## Reflection of point across x axis

In this concept, the x axis of the cartesian place act as a mirror.

So when we place a point around x axis, we get reflected image on the other side of the axis.

Note that the distance of reflected image from the x axis is same as the distance of original image.

For example, consider the below image.

Note that;
⟹ Original image lies at (-2, 1)

⟹ Red line is X axis which act as mirror

⟹ Reflected image is at (-2, -1)

Both the original & reflected image is equidistant from the central mirror axis.

### Shortcut rules for reflection of point over x axis

The following shortcut rules will help you to find the reflection of point along x axis.

To locate the reflected point location;

(a) retain the x coordinate of original point

(b) change the sign of y coordinate of original point

After following the above steps, you will get the located of reflected image of the point.

Let us understand the above rules with examples;

Example 01
The point (3, 5) is reflected along x axis. Locate the position of reflected image.

Solution
Following the above rules, if the point is reflected along x axis then;

⟹ Retain the position of x coordinate
⟹ change the sign of y coordinate

Hence the location of reflected point is ( 3, -5)

Given below is the position of image in graphical form.

In the above image;

⟹ Original Point ( 3, 5 )
⟹ Red line is x axis which is mirror
⟹ Reflected Image ( 3, -5)

Example 02
The point (-3, -2) is reflected along x axis. Locate the position of reflected image.

Solution
Since the point is reflected along x axis, the reflected image contain:

⟹ same x coordinate
⟹ y coordinate with different sign.

Hence, the location of reflected image is (-3, 2)

Plotting the images in graph diagram.

In the above image;
⟹ Original Point ( -2, -3 )
⟹ Red line is x axis which is mirror
⟹ Reflected Image ( -2, 3)

### Reflection of Image across x axis

You can also use above mentioned rules to draw the reflected image of simple geometrical figure.

Given below is the example of plotting reflected image of triangle along x axis.

The above image contains triangle with coordinates A (-4, 3), B (-4, 1) and C (-2, 1).

Now use the above mentioned x axis mirror rule to identify the position of reflected points.

The rule says to retain the x coordinate and change the sign of y coordinate.

⟹ (-4, 3) reflected image is (-4, -3)

⟹ (-4, 1) reflected image is (-4, -1)

⟹ (-2, 1) reflected image is (-2, -1)

Plotting the reflected points in cartesian graph, we get;

Join all the points and we will get the reflected image.