Everything Maths Grade 11

16.6 CHAPTER 16. GEOMETRY

Point x-coordinate y-coordinate

A B C D E F G H

�

�

�

�

�

� � �

A

D C B

E

F G

H

What do you notice about the x-coordinates? What do you notice about the y-coordinates?

What would happen tothe coordinates of point A, if it was rotated to theposition of point E?

What about point F rotated to the positionof B?

From these activities youshould have come to thefollowing conclusions:

• 90 ◦clockwise rotation:
  The image of a point P(x; y) rotated clockwise
  through 90 ◦around the origin is P�(y;−x).
  We write the rotation as (x; y)→ (y;−x).

x

y

P(x;y)

P�(y;−x)

�

�

• 90 ◦anticlockwise rotation:
  The image of a point P(x; y) rotated anticlockwise
  through 90 ◦around the origin is P�(−y; x).
  We write the rotation as (x; y)→ (−y; x).

x

y

P(x;y)

P��(−y;x)�

�

• 180 ◦rotation:
  The image of a point P(x; y) rotated through 180 ◦
  around the origin is P�(−x;−y).
  We write the rotation as (x; y)→ (−x;−y).

x

y

P(x;y)

P���(−x;−y)

�

�

Exercise 16 - 4

1. For each of the following rotations about the origin:
   (i) Write down the rule.
   (ii) Draw a diagram showing the direction of rotation.

(a) OA is rotated to OA�with A(4;2) and A�(−2;4)

(b) OB is rotated to OB�with B(−2;5) and B�(5;2)