ROTATION TRANSFORMATION IN GEOMETRY

Rotation transformation is one of the four types of transformations in geometry.

We can use the following rules to find the image after 90°, 180°, 270° clockwise and  counterclockwise rotation. 

Rules on Finding Rotated Image

90° Rotation (clock wise)

90° Rotation (counter clock wise)

180° Rotation (clock wise and counter clock wise)

Once students understand the rules which they have to apply for rotation transformation, they can easily make rotation transformation of a figure.

For example, if we are going to make rotation transformation of the point (5, 3) about 90° (clock wise rotation), after transformation, the point would be (3, -5).

Here the rule we have applied is (x, y) ------> (y, -x). 

So we get ( 5, 3 ) -------> ( 3, -5 ).

Let us consider the following example to have better understanding of reflection.

Question :

Let A ( -2, 1), B (2, 4) and C (4, 2) be the three vertices of a triangle. If this triangle is rotated about 90° clockwise, what will be the new vertices A' , B' and C' ?

Solution :

Step 1 :

First we have to know the correct rule that we have to apply in this problem.

Step 2 :

Here triangle is rotated about 90° clock wise. So the rule that we have to apply here is (x , y) -------> (y , -x)

Step 3 :

Based on the rule given in step 1, we have to find the vertices of the reflected triangle A'B'C'

Step 4 :

(x, y) -----> (y, -x)

A(-2, 1) -------> A'(1, 2)

B(2, 4) -------> B'(4, -2)

C(4, 2) -------> C'(2, -4)

Step 5 :

Vertices of the reflected triangle are

A'(1, 2), B(4, -2) and C'(2, -4)  

How to sketch the rotated figure ?

1. First we have to plot the vertices of the pre-image.

2. In the above problem, the vertices of the pre-image are

A(-2, 1), B(2, 4) and C(4, 2)

3. When we plot these points on a graph paper, we will get the figure of the pre-image (original figure).

4. When we rotate the given figure about 90° clock wise, we have to apply the formula

(x, y) -------> (y, -x) 

5. When we apply the formula, we will get the following vertices of the image (rotated figure).

6. In the above problem, vertices of the image are

A'(1, 2), B'(4, -2)  and C'(2, -4)

7. When plot these points on the graph paper, we will get the figure of the image (rotated figure).

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