Rotations of ± 90° and ± 180°

1. Consider the point (1;9) shown in the sketch.

1.1. The image of (1;9)rotated 90° anti-clockwise will become (-9;1).
Generally:

• 90° anti-clockwise or 90°becomes
• (x;y) → (-y;x)

1.2. The image of (1;9) rotated 90° clockwise will become (9;-1).
Generally:

• 90° clockwise or -90° becomes
• (x;y) → (y;-x)

1.3. The image of (1;9) rotated 180° anti-clockwise or clock-wise will become (-1;-9).

Generally:

• 180° clockwise or anti-clockwise
• (x;y) → (-x;-y)

1.4. 360° clockwise or anti-clockwise rotation through the origin leaves the figure or point unchanged.

Tutorial

1. Write down the co-ordinates of the given points
    A(7;2)
    B(3;8)
    C(2;5)
    D(-2;6)
    E(-3;-5)
if they are rotated :

1.1. 90° clockwise about the origin.

1.2. 90° anti-clockwise about the origin

1.3. 180° clockwise about the origin.

1.4. 180° anti-clockwise about the origin.

1.5. 360° clockwise about the origin.

1.6. 360° anti-clockwise about the origin.