# 90 Degree Clockwise Rotation

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).

Worked-out 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 co-ordinates 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

Lines of Symmetry

Point Symmetry

Rotational Symmetry

Order of Rotational Symmetry

Types of Symmetry

Reflection

Reflection of a Point in x-axis

Reflection of a Point in y-axis

Reflection of a point in origin

Rotation

90 Degree Clockwise Rotation

90 Degree Anticlockwise Rotation

180 Degree Rotation

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