How to Find the Shortest Distance
Mathematicians use specific techniques and formulas to find the shortest distance between a point and a line. Given certain knowledge about the line and the point, you can plug information into the necessary formula and perform a series of mathematical calculations to find the correct answer. You can also use computer software to find the shortest distance between the points or lines, or between two line segments in two-dimensional or three-dimensional space.
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Instructions
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Note the point coordinates (m, n in this example) and define the line using the standard line equation Ax + By + C = 0. For example, your point coordinates may be (2, 4) and your line might be defined by the equation 6x + 3y + 5 = 0.
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Use the formula to calculate the shortest distance between the point and the line. This equation is the A value of the line multiplied by point coordinate m, plus the B value of the line multiplied point coordinate n, plus the C value of the line, all divided by the root of A squared plus B squared.
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Plug your point's m and n coordinates along with the A, B and C values of the line and solve the equation, making sure you use the correct order of operations to guarantee that you don't make any errors when you are using the distance formula. Using the above example, you would multiply 6 x 2 and 3 x 4, adding the products (12 and 12) to the C value of the line, which is 5 to yield a sum of 29. Then, take the square root of A squared (36) plus B squared (9) and divide it into 29. The approximate quotient in this is example (29 divided by the square root of 45) is 4.32.
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Tips & Warnings
You can use computer software to find the shortest distance between any point and any line as well as to perform more complex calculations, such as the shortest distance between a point and a plane and the shortest distance between two lines in either two-dimensional or three-dimensional space.
References
- Photo Credit algebra image by Katrina Miller from Fotolia.com
