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.
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)
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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