What Is 90 Degree Clockwise Rotation?
A figure rotated about a fixed point in the clockwise direction by 90 degrees on a coordinate plane is called 90 degree clockwise rotation. So here the angle of rotation is 90 degrees.
The figure or the point is rotated about a fixed point called the center of rotation. In this article, we will take the origin as the center of rotation.
90 Degree Clockwise Rotation of a Point
Let’s rotate the point A(x,y) 90 degrees in a clockwise direction about the origin, O.
The new coordinates of the point are A’(y,-x).
To rotate any point by 90 degrees in clockwise direction we can follow three simple steps:
Step 1: Plot the point on a coordinate plane
Step 2: Rotate the point through 90 degrees in a clockwise direction about the origin
Step 3: Note the coordinates of the new location of the point
90 Degree Clockwise Rotation of a Figure
To rotate a figure 90 degrees clockwise, rotate each vertex of the figure in clockwise direction by 90 degrees about the origin.
Let’s consider the rotation of rectangle ABCD in the figure:
The vertices of the rectangle are A(-3, -3), B(1, -3), C(1, -5) and D(-3 ,-5). Let’s apply 90 degree clockwise rotation about the origin to each of these vertices.
A(-3, -3) → A’(-3, 3)
B(1, -3) → B’(-3, -1)
C(1, -5) → C’(-5, -1)
D(-3, -5) → D’(-5, 3)
Plot the points A’, B’, C’ and D’ on the same coordinate plane and draw a rectangle A’B’C’D’.
So, A’B’C’D’ is the required rotated figure.
[Note: In rotation, the original figure and the rotated figure are identical.]
Solved Examples
Example 1: Rotate the following points 90 degrees clockwise.
a. (1, 3)
b. (-5, 2)
c. (4, 9)
d. (-8, 0)
Solution:
a. (1, 3)
So, (1,3) rotated 90 degrees clockwise is (3,-1).
b. (-5, 2)
So, (-5, 2) rotated 90 degrees clockwise is (2, 5).
c. (4, 9)
So, (4, 9) rotated 90 degrees clockwise is (9, -4).
d. (-8, 0)
So, (-8, 0) rotated 90 degrees clockwise is (0, 8).
Example 2: The vertices of a triangle are (1, 1), (2, 8) and (-4, 5). Jacob finds the coordinates of the vertices of the triangle after 90 degrees clockwise rotation.
Is Jacob correct?
Solution:
Rotate each vertex of the triangle by 90 degrees in clockwise direction.
(1, 1) → (1, -1),
(2, 8) → (8, -2) and
(-4, 5) → (5, 4).
The vertices of the new figure are (1, -1), (8, -2) and (5, 4).
So, Jacob is not correct in finding the coordinates of the triangle rotated 90 degrees clockwise.
The number of degrees by which a point or a figure is rotated on the coordinate plane is called the angle of rotation.
A clockwise rotation of n degrees is the same as (360 – n) degrees in terms of counterclockwise rotation. So, a 90 degree clockwise rotation is the same as a 270 degree counterclockwise rotation.
The new position of point (2, 3) after 90 degrees clockwise rotation is (3, -2).