Reflection

Answer:

It is a transformation which produces a mirror image of an object. The mirror image can be either about x-axis or y-axis. The object is rotated by180°.

Types of Reflection:

Reflection about the x-axis
Reflection about the y-axis
Reflection about an axis perpendicular to xy plane and passing through the origin
Reflection about line y=x

1. Reflection about x-axis: The object can be reflected about x-axis with the help of the following matrix

Reflection

In this transformation value of x will remain same whereas the value of y will become negative. Following figures shows the reflection of the object axis. The object will lie another side of the x-axis.

Reflection

2. Reflection about y-axis: The object can be reflected about y-axis with the help of following transformation matrix

Reflection

Here the values of x will be reversed, whereas the value of y will remain the same. The object will lie another side of the y-axis.

The following figure shows the reflection about the y-axis

Reflection

3. Reflection about an axis perpendicular to xy plane and passing through origin:
In the matrix of this transformation is given below

Reflection

In this value of x and y both will be reversed. This is also called as half revolution about the origin.

4. Reflection about line y=x: The object may be reflected about line y = x with the help of following transformation matrix

Reflection

First of all, the object is rotated at 45°. The direction of rotation is clockwise. After it reflection is done concerning x-axis. The last step is the rotation of y=x back to its original position that is counterclockwise at 45°.

Example: A triangle ABC is given. The coordinates of A, B, C are given as

A (3 4)
B (6 4)
C (4 8)

Find reflected position of triangle i.e., to the x-axis.

Solution:

Reflection