Distance from a point to a line - 2-Dimensional.
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(Mx, My) and line can be found using the following formula
|d =|||A·Mx + B·My + C||
|√A2 + B2|
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|
|√32 + 42||√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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