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Coordinate Plane

Sep 14, 2022
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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. 

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 

parallel
  • 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. 

rotation in different quadrants

Rotations in the coordinate plane about the origin 

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 

Rotation of 90° counter-clockwise about the origin 

Example 2 

Rotation of 180° about the origin 

parallel
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) 

Coordinates of the point after transformation or rotation 

Example 4 

Coordinates of the point after transformation or rotation 

A’(3, 3), B(7, –5), C(10, –10) 

Coordinates of the point after transformation or rotation 

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) 

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.
5. Rotate the figure 90° counter-clockwise and write the coordinates.

6. Rotate the figure 180° 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) 

The points are R’ (-3, 1), S’(-4, 4), T’(4, 1) 
1. Quadrilateral MATH has the following coordinate points: M (6,5) A (9,12) T (8,-2) H(0,0). Find the coordinates of the image after the given rotation:
2. 90°C W. Give the coordinates after rotation. T (5,2), I (4,0), H (-1,6), G (2,8)
3. 180° CW. Give the coordinates after rotation. M (2,0), T (3,2), A (-3, 4), and R (7,-1)
4. Rotate LEG 90° CW from the origin. Call it L’E’G’.

Concept Map 

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