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Distance from point to plane.

Distance from point to plane
Definition.
The distance from a point to a plane is equal to length of the perpendicular lowered from a point on a plane.

Distance from point to plane formula

If Ax + By + Cz + D = 0 is a plane equation, then distance from point M(Mx, My, Mz) to plane can be found using the following formula:

d |A·Mx + B·My + C·Mz + D|
A2 + B2 + C2

Examples of tasks with distance from point to plane

Example 1.
To find a distance between plane 2x + 4y - 4z - 6 = 0 and point M(0, 3, 6).

Solution. Let's use the formula

d |2·0 + 4·3 + (-4)·6 - 6|  =  |0 + 12 - 24 - 6|  =  |- 18|  = 3
4 + 16 + 16 36 6

Answer: Distance from point to plane is equal to 3.

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