90 Degree Anticlockwise Rotation

Learn about the rules for 90 degree anticlockwise rotation about the origin.

How do you rotate a figure 90 degrees in anticlockwise direction on a graph?

Rotation of point through 90° about the origin in anticlockwise direction when point M (h, k) is rotated about the origin O through 90° in anticlockwise direction. The new position of point M (h, k) will become M' (-k, h).

$90° Anticlockwise Rotation$

Worked-out examples on 90° anticlockwise rotation about the origin:

1. Find the new position of the following points when rotated through 90° anticlockwise about the origin.

(i) A (2, 3)

(ii) B (-5, -7)

(iii) C (-6, 9)

(iv) D (4, -8)

Solution:

When rotated through 90° about the origin in anticlockwise direction. The new positions of the above points are:

(i) The new position of point A (2, 3) will become A' (-3, 2)

(ii) The new position of point B (-5, -7) will become B' (7, -5)

(iii) The new position of point C (-6, 9) will become C' (-9, -6)

(iv) The new position of point D (4, -8) will become D' (8, 4)

2. Draw a triangle ABC on the graph paper. The co-ordinate of A, B and C being A (1, 2), B (3, 1) and C (2, -2), find the new position when the triangle is rotated through 90° anticlockwise about the origin.

Solution:

$90 Degree Anticlockwise Rotation$

Plot the points A (1, 2), B (3, 1) and C (2, -2) on the graph paper. Join AB, BC and Cato get a triangle. On rotating it through 90° about the origin in anticlockwise direction, the new position of the points are:

A (1, 2) will become A' (-2, 1)

B (3, 1) will become B' (-1, 3)

C (2, -2) will become C' (2, 2)

Thus, the new position of ∆ ABC is ∆ A'B'C'.

● Related Concepts

● Lines of Symmetry

● Point Symmetry

● Rotational Symmetry

● Order of Rotational Symmetry

● Types of Symmetry

● Reflection

● Reflection of a Point in x-axis