In this chapter we will learn the concept of reflection over y axis with solved examples.

Let us first review the basics of reflection.

## What is Reflection in Math ?

The **object’s mirror image** is known as **reflection**.

The reflected image **shows following property;**

(a) Reflected image is flipped in orientation.

(b) the reflected image is of same size and dimension as that of original image.

(c) Both the original and reflected image are equidistant from the central mirror axis.

## Reflection of point across y axis

In this concept, the **vertical y axis** of cartesian plane **act as the mirror**.

When we place object in front of y axis we get the reflected image in opposite direction.

For example, consider the below image.

Note that;

⟹ Original image lies at (-2, 3)

⟹ Y axis (shown in red color) act as mirror line

⟹ Reflected image lies in (2, 3)

Also, both the original and reflected image is equidistant from y axis.

### Shortcut rule for reflection of point over y axis

The following steps will help you find the **location of reflected image from y axis**.

To locate the position of reflected point, follow the below steps;

⟹ **change the sign of x coordinate** of original point

⟹ **retain the same y coordinate**

Let us understand the above steps with following examples;

**Example 01**

The point ( -1, 2 ) is reflected along y axis. Find the location of reflected image.

**Solution**

When the point is reflected along y axis, follow the below rules;

⟹ change the sign of x coordinates

⟹ retain y coordinates

Hence, the location of reflected point is (1, 2).

Plotting the above points in graphical image.

In the above image;

⟹ Original Point ( -1, 2 )

⟹ Y axis line is the mirror line

⟹ Reflected Point ( 1, 2 )

**Example 02**

The point (3, -4) is reflected along y axis. Find the location of reflected image.

**Solution**

Since the point is reflected along y axis, the reflected image contain;

⟹ x coordinate with different sign

⟹ same y coordinate

Hence, the location of reflected image is (-3, -4)

Plotting the images in graph diagram.

In the above image;

⟹ Original Point (3, -4)

⟹ Red line is the mirror axis

⟹ Reflected Point (-3, -4)

### Reflection of Image across Y axis

Similar to point reflection, you can **reflect simple geometrical shape** **along y axis** by following below steps;

(a) Mark all the vertex of given shape.

(b) Find the location of reflected image of each vertex point.

(c) Now join all the reflected point to get the reflected shape.

Let us understand the above steps with the help of example.

**Example 01**

Draw the reflected image of following shape.

**Solution**

To plot the reflected image of above quadrilateral, follow the below steps;

**(a) Mark the location of all vertex**

The given quadrilateral has coordinates A (-5, 7), B (-4, 6), C (-5, 4) and D (-7, 5)

**(b) Now locate the reflected points of all the vertes.**

Since, the image is reflected along y axis, we will change the sign of x coordinates and retain the y coordinates to get the reflected points.

⟹ (-5, 7) reflected image is (5, 7)

⟹ (-4, 6) reflected image is (4, 6)

⟹ (-5, 4) reflected image is (5, 4)

⟹ A(-7, 5) reflected image is (7, 5)

Plotting all the reflected point is graphical figure.

Join all the reflected points to get the reflected image.