# Distance from point to plane.

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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(M_{x}, M_{y}, M_{z}) to plane can be found using the following formula:

d = | |A·M_{x} + B·M_{y} + C·M_{z} + D| |

√A^{2} + B^{2} + C^{2} |

## 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.

Analytic geometry: Introduction and contentsDistance between two pointsMidpoint. Coordinates of midpointEquation of a lineEquation of a planeDistance from point to planeDistance between two planesDistance from a point to a line - 2-DimensionalDistance from a point to a line - 3-DimensionalAngle between two planesAngle between line and plane

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