In this chapter we will learn how to rotate a point counterclockwise by 270 degrees around the origin.
Counterclockwise 270 degrees rotation of a point
We will understand the concept with the help of example.
Consider the below point A located at coordinates (2, 3).
We have to rotate the point A by 270 degree in counterclockwise direction
First find the angle formed by point A with horizontal axis.
So the point A forms 123 degree with the horizontal line.
i.e. ∠AOX = 123 degree
To rotate the point by 270 degrees, we have to extend the angle by 147 degrees.
i.e. 270 – 123 = 147 degree
If we add both the angles we will get total angle of 270 degrees.
Now take a divider and sets its length to OA.
Place one leg of the divider at O and cut an arc on line z.
The point formed on the line z is the rotated point A.
Hence, the point A (2, 3) is rotated by 270 degree anticlockwise direction to reach point B (3, -2).
Coordinates after 270 degree counterclockwise rotation- Shortcut method
If a point is rotated by 270 degree anticlockwise direction, the coordinates for final points is given by following method.
Let (m, n) be the initial point. If we rotate the given point by 270 degree counterclockwise direction, then its final coordinates will be (n, -m)
Hence, Initial point ⟹ (m, n)
270 degree rotated point ⟹ (n, -m)
Let us understand the method with examples.
Example 01
The point (3, 4) is rotated by 270 degree anticlockwise direction. Find the coordinates of final point.
Solution
Initial Point ⟹ (3, 4)
Final Point ⟹ (4, -3)
Plotting the rotation in graphical image.
Example 02
The point (-2, 4 ) is rotated by 270 degree in counterclockwise direction. Find the coordinates of final point.
Solution
Initial Point ⟹ (-2, 4)
Final Point ⟹ (4, 2)
Plotting the rotation in graphical image.
Example 03
The point (-2, -1) is rotated by 270 degree in counterclockwise direction around the origin. Find the coordinates of final point.
Solution
Initial Point ⟹ (-2, -1)
Final Point ⟹ (-1, 2)
Plotting the rotation in graphical image.
How to rotate the object by 270 degree in counterclockwise direction
Follow the below steps;
(a) Find coordinate points of all vertex of given figure.
(b) Now rotate all vertex points by 270 degree anti-clockwise as explained above.
(c) Find the coordinate points of all vertex of the rotated figure.
(d) Join the rotated vertex to form the figure.
Let us understand the above method with example.
Example 01
Rotate the below quadrilateral anticlockwise by 270 degree.
Solution
Let’s find the coordinates for rotated vertices using above mentioned shortcut method.
(2, 1) rotated point is (1, -2)
(1, 2) rotated point is (2, -1)
(2, 3) rotated point is (3, -2)
(3, 2) rotated point is (2, -3)
Joining all the rotated point in the graphical figure.
(02) Rotate the below shape by 270 degree counterclockwise.
Solution
Find the rotated points for each of the vertices using the shortcut method described above.
(-6, 2) rotated point is (2, 6)
(-6, 3) rotated point is (3, 6)
(-4, 3) rotated point is (3, 4)
(-4, 4) rotated point is (4, 4)
(-3, 4) rotated point is (4, 3)
(-3, 1) rotated point is (1, 3)
(-4, 1) rotated point is (1, 4)
(-4, 2) rotated point is (2, 4)
Joining all the reflected vertex in graphical figure.
Example 03
Rotate the given figure by 270 degree anticlockwise direction around the origin.
Solution
Let’s find the coordinates for the rotated vertex.
(-3, -3) rotated point is (-3, 3)
(-2, -3) rotated point is (-3, 2)
(-1, -4) rotated point is (-4, 1)
(-4, -4) rotated point is (-4, 4)
Joining all the vertex in graphical image.
