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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