Learn about the rules for 90 degree clockwise rotation about the origin.
How do you rotate a figure 90 degrees in clockwise direction on a graph?
Rotation of point through 90° about the origin in clockwise direction when point M (h, k) is rotated about the origin O through 90° in clockwise direction. The new position of point M (h, k) will become M’ (k, h).
Workedout examples on 90 degree clockwise rotation about the origin:
1. Plot the point
M (2, 3) on the graph paper and rotate it through 90° in clockwise direction,
about the origin. Find the new position of M.
Solution:
When the point is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M' (k, h).
Therefore, the new position of point M (2, 3) will become M' (3, 2).
2. Find the coordinates of the points obtained on rotating the point given below through 90° about the origin in clockwise direction.
(i) P (5, 7)
(ii) Q (4, 7)
(iii) R (7, 5)
(iv) S (2, 5)
Solution:
When rotated through 90° about the origin in clockwise direction, the new position of the above points are;
(i) The new position of point P (5, 7) will become P' (7, 5)
(ii) The new position of point Q (4, 7) will become Q' (7, 4)
(iii) The new position of point R (7, 5) will become R' (5, 7)
(iv) The new position of point S (2, 5) will become S' (5, 2)
`3. Construct the image of the given figure under the rotation of 90° clockwise about the origin O.
Solution:
We get rectangular PQRS by plotting the points P (3, 1), Q (3, 1), R (3, 1), S (3, 1). When rotated through 90°, P' (1, 3), Q' (1, 3), R' (1, 3) and S' (1, 3).
Now join P'Q'R'S'.
Therefore, P'Q'R'S' is the new position of PQRS when it is rotated through 90°.
4. Draw a quadrilateral PQRS joining the points P (0, 2), Q (2, 1), R (1, 2) and S (2, 1) on the graph paper. Find the new position when the quadrilateral is rotated through 90° clockwise about the origin.
Solution:
Plot the point P (0, 2), Q (2, 1), R (1, 2) and S (2, 1) on the graph paper. Now join PQ, QR, RS and SP to get a quadrilateral. On rotating it through 90° about the origin in clockwise direction, the new positions of the points are
The new position of point P (0, 2) will become P' (2, 0)
The new position of point Q (2, 1) will become Q' (1, 2)
The new position of point R (1, 2) will become R' (2, 1)
The new position of point S (2, 1) will become S' (1, 2)
Thus, the new position of quadrilateral PQRS is P'Q'R'S'.
`● Related Concepts
● Order of Rotational Symmetry
● Reflection of a Point in xaxis
● Reflection of a Point in yaxis
● Reflection of a point in origin
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
7th Grade Math Problems
8th Grade Math Practice
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