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The distance formula is a fundamental concept in mathematics that allows us to calculate the length of a line segment. Whether in geometry, physics, or engineering, understanding how to use the distance formula is crucial in solving various problems and analyzing spatial relationships. By utilizing the principles of coordinate geometry, the distance formula provides a straightforward approach to determine the distance between two points in a Cartesian plane. This introduction will explore the step-by-step process of using the distance formula and highlight its significance in measuring the lengths of line segments accurately.
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We can measure the length of a line segment or horizontal line on the coordinate plane simply by counting the coordinates; however, finding the length of a diagonal is more difficult. You can use the distance formula to find the length of a line. The distance formula is a generalized case of the Pythagorean Theorem, you can think of a given line segment as the hypotenuse of a right triangle. [1] XResearch Source By applying basic formulas in geometry, it becomes quite easy to calculate the length of a line in the coordinate plane.
Steps
Formula setting
![Image titled Use Distance Formula to Find the Length of a Line Step 1](https://www.wikihow.com/images_en/thumb/b/b7/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-1-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-1-Version-2.jpg)
![Image titled Use Distance Formula to Find the Length of a Line Step 2](https://www.wikihow.com/images_en/thumb/0/09/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-2-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-2-Version-2.jpg)
- The horizontal axis is the horizontal axis; The vertical axis is the vertical axis.
- The coordinates of a point are shown as follows (x,y){displaystyle (x,y)} .
- For example, a line segment can be specified by the point (2,first){displaystyle(2,1)} and (6,4){displaystyle(6,4)} .
![Image titled Use Distance Formula to Find the Length of a Line Step 3](https://www.wikihow.com/images_en/thumb/8/8f/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-3-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-3-Version-2.jpg)
- For example, we have points (2,first){displaystyle(2,1)} and (6,4){displaystyle(6,4)} , the formula becomes: d=(6−2)2+(4−first)2{displaystyle d={sqrt {(6-2)^{2}+(4-1)^{2}}}}
Calculate the length
![Image titled Use Distance Formula to Find the Length of a Line Step 4](https://www.wikihow.com/images_en/thumb/5/52/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-4-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-4-Version-2.jpg)
- For example:
d=(6−2)2+(4−first)2{displaystyle d={sqrt {(6-2)^{2}+(4-1)^{2}}}}
d=(4)2+(3)2{displaystyle d={sqrt {(4)^{2}+(3)^{2}}}}
![Image titled Use Distance Formula to Find the Length of a Line Step 5](https://www.wikihow.com/images_en/thumb/a/a5/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-5-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-5-Version-2.jpg)
- For example:
d=(4)2+(3)2{displaystyle d={sqrt {(4)^{2}+(3)^{2}}}}
d=16+9{displaystyle d={sqrt {16+9}}}
![Image titled Use Distance Formula to Find the Length of a Line Step 6](https://www.wikihow.com/images_en/thumb/d/dd/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-6-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-6-Version-2.jpg)
- For example:
d=16+9{displaystyle d={sqrt {16+9}}}
d=25{displaystyle d={sqrt {25}}}
![Image titled Use Distance Formula to Find the Length of a Line Step 7](https://www.wikihow.com/images_en/thumb/7/7e/Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-7-Version-2.jpg/v4-728px-Use-Distance-Formula-to-Find-the-Length-of-a-Line-Step-7-Version-2.jpg)
- Since we’re looking for the square root, you may need to round your answer.
- Since this is a problem on the coordinate plane, the answer will be “common units”, not centimeters, meters or other metric units.
- For example:
d=25{displaystyle d={sqrt {25}}}
d=5{displaystyle d=5}
Advice
- Avoid confusing this formula with other formulas such as the formula for finding the coordinates of the midpoint, calculating the slope of a line, the equation of a straight line, or a linear equation.
- Remember the order in which calculations are performed when doing math. Subtract first, then square the differences, then add, and finally find the square root.
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 435,809 times.
We can measure the length of a line segment or horizontal line on the coordinate plane simply by counting the coordinates; however, finding the length of a diagonal is more difficult. You can use the distance formula to find the length of a line. The distance formula is a generalized case of the Pythagorean Theorem, you can think of a given line segment as the hypotenuse of a right triangle. [1] XResearch Source By applying basic formulas in geometry, it becomes quite easy to calculate the length of a line in the coordinate plane.
In conclusion, the distance formula is an essential tool in mathematics to determine the length of a line segment. By utilizing the formula, which is derived from the Pythagorean theorem, one can calculate the distance between any two points on a coordinate plane. The formula allows for precise measurements and is applicable in various fields such as geometry, physics, and engineering. By understanding and mastering the distance formula, individuals can accurately determine the lengths of line segments and solve a multitude of problems involving distance and position. With practice and application, this formula becomes a reliable method for measuring distances and is a fundamental concept in mathematics.
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