Coordinate Plane

Key Concept

• Rotation
• Rotations in a coordinate plane
• Describe rotation

Rotation 

The rotation occurs when we turn around a given point. We can define rotation as a transformation around a fixed point called the centre of rotation. 

Rotations can occur either clockwise or anti-clockwise. 

The figure does not change the size. 

The point (x, y) in different quadrants in the x y plane or coordinate plane. 

Understanding Rotations 

Rotation in different quadrants in a coordinate plane 

Let the image be in the first quadrant 

• If the image is moving in an anti-clockwise direction at 90°, it will move to the second quadrant, and if the image is moving in a clockwise direction at 90°, the image will move to the fourth quadrant. 

•   If the image is moving 180°, it will move to the third quadrant in both clockwise and anti-clockwise directions. 
• If the image is moving in an anti-clockwise direction at 270°, it will move to the fourth quadrant, and if the image is moving clockwise direction 270°, the image will move to the second quadrant. 
• The rotation of 360° would match the image with its preimage. 

Rules of rotation in different quadrants in a coordinate plane in both clockwise and counter-clockwise directions. 

Rotations in the coordinate plane about the origin 

Coordinates of the point after transformation or rotation of 90° and 180° around the origin. 

Example 1 

Rotation of 90° counter-clockwise about the origin 

Example 2 

Rotation of 180° about the origin 

Example 3 

Coordinates of the point after transformation or rotation 

V’(3, 2), E’(-2, 1), G’(0, 3) 

Example 4 

Coordinates of the point after transformation or rotation 

A’(3, 3), B(7, –5), C(10, –10) 

What did we discuss in this session? 

Based on the figure, answer the following: 

Points are R(1, 3), S(4, 4), T(2, 1) 

If the image is moving 90° clockwise, what will be the coordinates of R’S’T’? 

The points are R’ (3, -1), S’(4, -4), T’(1, -4) 

 If the image is moving 90° counter-clockwise, what will be the coordinate of R’S’T’? 

The points are R’ (-3, 1), S’(-4, 4), T’(4, 1) 

 If the image is moving 180° clockwise, what will be the coordinates of R’S’T’? 

The points are R’(-1, -3), S’(-4, -4), T’(-2, -1) 

 If the image is moving 180° counter-clockwise, what will be the coordinates of R’S’T’? 

The points are R’(-1, -3), S’(-4, -4), T’(-2, -1) 

 If the image is moving 270° counter-clockwise, what will be the coordinates of R’S’T’? 

Exercise:

• 1. Why rotation is called a rigid transformation?
• 2. In what quadrant will an image be if a figure is in quadrant II and is rotated 90° clockwise?
• 3. In what quadrant will an image be if a figure is in quadrant III and is rotated 180° clockwise?
• 4. In what quadrant will an image be if a figure is in quadrant I and is rotated 90° counterclockwise?
• 5. Rotate the figure 90° counter-clockwise and write the coordinates.

6. Rotate the figure 180° clockwise and write the coordinates.

The points are R’ (-3, 1), S’(-4, 4), T’(4, 1) 

Concept Map