Rotation on a airplane is determined by:
- Rotation midpoint point
- Large angle of rotation
- Direction of rotation angle
The administration of rotation is said to live on positive if it is anticlockwise as well as the administration of rotation is negative if it is handled alongside the hands of the clock.
1. Rotation alongside Center O (0, 0)
Rotation formula alongside the midpoint O(0, 0)
x' = 10 cos θ - y sin θy' = 10 sin θ + y cos θ
2. Rotation alongside midpoint P (a, b)
Rotational formula alongside midpoint P (a, b)
x' - a = (x - a) cos θ - (y - b) sin θy' - b = (x - a) sin θ + (y - b) cos θ
Example:
Please cause upwards one's hear the shadow from the holler for A(2, 3) when rotated past times the 90° corner counterclockwise alongside the midpoint P (1, -6)!
Answer:
Rotation 90° counterclockwise agency θ = 90°
x' - a = (x - a) cos θ - (y - b) sin θ
x' - 1 = (2 - 1) cos 90°- (-3 - (-6)) sin 90°
x' - 1 = cos 90° - iii sin 90°
x' - 1 = 0 - 3
x' - 1 + 1 = -3 + 1
x' = -2
y' - b = (x - a) sin θ + (y - b) cos θ
y' - (-6) = (2 - 1) sin 90° + (-3 - (-6)) cos 90°
y' + half dozen = sin 90° + iii cos 90°
y' + half dozen = 1 + 0
y' + half dozen - half dozen = 1 - 6
y' = -5
So the shadow coordinates are A'(- 2, -5).
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