In this chapter we will how to rotate a point by 270 degrees clockwise direction about the origin.
We will also look at the solved problems for better conceptual understanding.
Clockwise 270 degree rotation of point
We will understand the concept with the help of an example.
Consider the point A with coordinate (-2, 3) in the below image.
We will rotate the point clockwise by 270 degree around the origin.
Let us find the angle made by point A with respect to horizontal axis.
Hence, the point make angle 123 degree around the origin.
i.e. ∠AOX = 123 degree.
To make 270 degree rotation, we have to extend the existing angle by 147 degree.
i.e. 270 – 123 = 147 degree.
If we add up the above two angles we will get 270 degree angle.
Here, ∠YOA = 270 degree.
Now take a divider and set its length equal to OA.
Place one leg of divider on point O and cut an arc on line y.
The point marked on line y is the rotated point A by 270 degree.
I hope you understood the above process.
Let us now look at the shortcut method to find the coordinates of point rotated by 270 degree clockwise.
Shortcut for 270 degree clockwise rotation
If a point is rotated by 270 degree around the origin in clockwise direction, the coordinates of final point is given by following method.
If (h, k) is the initial point, then after 270 degree clockwise rotation, the location of final point is (-k, h)
Hence,
Original Point ⟹ (h, k)
270 degree rotated point ⟹ (-k, h)
Note;
The formula is similar to 90 degree anticlockwise rotation.
Since, 270 degree clockwise rotation = 90 degree counterclockwise rotation, both the movements will result in same final coordinate.
Let us look at solved examples for better understanding of the concept.
Example 01
The point (3, 1) is rotated by 270 degrees in clockwise direction. Find the location of rotated point.
Solution
Initial Point ⟹ (3, 1)
Final rotated point ⟹(-1, 3)
Plotting the rotation in graphical image.
Example 02
The point (2, -4) is rotated 270 degree in clockwise direction. Find the coordinates of final point.
Solution
Initial Point ⟹ (2, -4)
Final rotated point ⟹(4, 2)
Showing the rotation in graphical image.
Example 03
The point (-2, -2) is rotated 170 degree in clockwise direction. Find the location of rotated point.
Solution
Initial Point ⟹ (-2, -2)
Final rotated point ⟹(2, -2)
Showing the rotation in graphical image.
How to rotate the object by 270 degree clockwise direction ?
You can easily rotate simple geometrically objects by following the below steps;
(a) Locate the vertex of given figure
(b) Now rotate each vertex individually
(c) Find the location of rotated vertex and join all the points
Let us understand the steps with the help of below example.
Example 01
Rotate the below triangle by 270 degree in clockwise direction around the origin.
Solution
Finding the location of all rotated vertex using the above mentioned shortcut method.
(3, -1) rotated point is (1, 3)
(2, -3) rotated point is (3, 2)
(1, -2) rotated point is (2, 1)
Plotting all the rotated points and joining them to get the rotated figure.
