In this chapter we will learn to rotate point and object by 90 degree along the origin.
We will also look at the solved examples for conceptual clarity at the end of the chapter.
Let us first review the basics of rotation.
What is Rotation ?
When an object is moved around the central point or axis then the movement is called rotation.
For example;
The moon around the center object called earth. The movement of moon is called Rotation.
The full circle rotation of moon around earth is called 360 degree rotation.
Moving point in 90 degree clockwise rotation
Here we will learn to rotate a point at 90 degree clockwise rotation.
Consider the below image of cartesian coordinate.
The location of point A is (2, 3).
We have to rotate point A along point at 90 degree clockwise direction.
Let us find the angle of OA with respect to horizontal axis.
Here the point A form 56 degree angle with horizontal axis.
i.e. ∠XOA = 56 degree.
Since we need point with 90 degree angle of rotation, we need to add 34 degree more in the existing angle.
Here we have extended the angle by 34 degree.
If we remove the horizontal line, we will get angle of 90 degree.
Now we have to find the location of rotated point A.
Take a divider and set its length equal to OA.
Now place one leg of divider at point O and cut an arc at line L.
Here the located of rotated point is (3, -2)
Hence the point A is rotated 90 degree clockwise to reach point B.
The above method can be repeated to move any point clockwise around the central point O.
Shortcut for 90 degree clockwise rotation
In the cartesian plane, when a point is rotated 90 degree clockwise, the location of rotated point can be found by using following method.
If (h, k) is the original point, then after 90 degree clockwise rotation the rotated coordinate will be (k, -h).
Hence,
Original Point ⟹ (h, k)
90 degree clockwise rotated point ⟹ (k, -h)
Let us solve some example for better understanding.
Example 01
If point (2, 3) is rotated clockwise by 90 degree around origin, find the location of new point.
Solution
Original Point Coordinate ⟹ (2, 3)
Coordinate for rotated point ⟹ (3, -2)
Given below is the graphical representation of both the points.
Example 02
The point (-4, -3) is rotated clockwise by 90 degree. Find the coordinates for rotated point.
Solution
Original Point Coordinate ⟹ (-4, -3)
Rotated Point coordinate ⟹ (-3, 4)
Observe the below graphical representation of rotated points.
Example 03
The point (2, -2) is rotated by 90 degree clockwise. Find the coordinate of the rotated point.
Solution
Original Point Coordinate ⟹ (2, -2)
Rotated Point coordinate ⟹ (-2, -2)
Given below is the graphical representation of the rotation.
Clockwise rotation of objects by 90 degree
You can clockwise rotate simple geometrical objects by 90 degree by following the below step;
(a) Locate the vertices of given figure.
(b) Now rotate each of the vertices individually.
(c) Use the above shortcut method to find the coordinates of rotated points.
(d) Join all the rotated points to form the complete figure.
Let us understand the above process with examples.
Example 01
Given below is the image of rectangle ABCD with coordinates. If the rectangle is rotated clockwise by 90 degree, find the coordinates of rotated image.
Solution
Since the rotation is done clockwise by 90 degree, we will use the above mentioned shortcut trick to calculated each rotated point.
(-6, 1) rotated point coordinate ⟹ (1, 6)
(-6, 3) rotated point ⟹ (3, 6)
(-3, 3) rotated point ⟹ (3, 3)
(-3, 1) rotated point ⟹ (1, 3)
Plotting the rotated points in graphical image.
(02) The given quadrilateral is rotated by 90 degree in clockwise direction. Find the coordinated of rotated image.
Solution
(2, 1) rotated point coordinate ⟹ (1, -2)
(2, 2) rotated point coordinate ⟹ (2, -2)
(3, 3) rotated point coordinate ⟹ (3, -3)
(4, 2) rotated point coordinate ⟹ (2, -4)
Join all the final coordinates to get the rotated image.
