# Distance from a point to a line - 2-Dimensional.

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Definition.

**Distance from a point to a line**— is equal to length of the perpendicular distance from the point to the line.

## Distance from a point to a line on plain formula

If Ax + By + C = 0 is 2D line equation, then distance between point M(M_{x}, M_{y}) and line can be found using the following formula

d = | |A·M_{x} + B·M_{y} + C| |

√A^{2} + B^{2} |

## Examples of tasks with from a point to a line on plain

Example 1.

To find distance between line 3x + 4y - 6 = 0 and point M(-1, 3).
**Solution.** Let's use the formula:

d = | |3·(-1) + 4·3 - 6| | = | |-3 + 12 - 6| | = | |3| | = 0.6 |

√3^{2} + 4^{2} |
√9 + 16 | 5 |

**Answer:** distance from point to line is equal to 0.6.

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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