Question:

Published on: 16 September, 2024

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°.

- 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

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.

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

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

**3. Reflection about an axis perpendicular to xy plane and passing through origin:**

In the matrix of this transformation is given below

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

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:**

The a point coordinates after reflection

The b point coordinates after reflection

The coordinate of point c after reflection

a (3, 4) becomes a^{1} (3, -4)

b (6, 4) becomes b^{1} (6, -4)

c (4, 8) becomes c^{1} (4, -8)

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