ROTATION TRANSFORMATION IN GEOMETRY
About the topic "Rotation transformation in geometry"
"Rotation transformation" is one of the four types of transformations in geometry.
Even though students can get this stuff on internet, they do not understand exactly what has been explained.
To make the students to understand the stuff "Rotation-transformation", we have explained the different rules which we apply to make rotation-transformation.
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).
After having gone through the stuff given above, we hope that the students would have understood "Rotation transformation".
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