Download Article
Download Article
Think of the distance between any two points as a line. The length of this line can be found by using the distance formula: .
Things You Should Know
- Jot down the coordinates that you're measuring the distance between.
- Plug these coordinates into the distance formula: .
- Solve the formula by squaring the differences of the x and y values, adding these differences together, and finding the square root of the remaining sum.
Steps
-
Take the coordinates of two points you want to find the distance between. Call one point Point 1 (x1,y1) and make the other Point 2 (x2,y2). It does not terribly matter which point is which, as long as you keep the labels (1 and 2) consistent throughout the problem. [1] X Research source
- x1 is the horizontal coordinate (along the x axis) of Point 1, and x2 is the horizontal coordinate of Point 2. y1 is the vertical coordinate (along the y axis) of Point 1, and y2 is the vertical coordinate of Point 2.
- For an example, take the points (3,2) and (7,8). If (3,2) is (x1,y1), then (7,8) is (x2,y2).
-
Know the distance formula . This formula finds the length of a line that stretches between two points: Point 1 and Point 2. The linear distance is the square root of the square of the horizontal distance plus the square of the vertical distance between two points. [2] X Research source More simply put, it is the square root of:Advertisement
-
Find the horizontal and vertical distance between the points. First, subtract y2 - y1 to find the vertical distance. Then, subtract x2 - x1 to find the horizontal distance. Don't worry if the subtraction yields negative numbers. The next step is to square these values, and squaring always results in a positive number. [3] X Research source
- Find the distance along the y-axis. For the example points (3,2) and (7,8), in which (3,2) is Point 1 and (7,8) is Point 2: (y2 - y1) = 8 - 2 = 6. This means that there are six units of distance on the y-axis between these two points.
- Find the distance along the x-axis. For the same example points (3,2) and (7,8): (x2 - x1) = 7 - 3 = 4. This means that there are four units of distance separating the two points on the x-axis.
-
Square both values. This means that you will square the x-axis distance (x2 - x1), and that you will separately square the y-axis distance (y2 - y1).
-
Add the squared values together. This will give you the square of the diagonal, linear distance between your two points. In the example of the points (3,2) and (7,8), the square of (8 - 2) is 36, and the square of (7 - 3) is 16. 36 + 16 = 52.
-
Take the square root of the equation. This is the final step in the equation. The linear distance between the two points is the square root of the sum of the squared values of the x-axis distance and the y-axis distance. [4] X Research source
- To carry on the example: the distance between (3,2) and (7,8) is sqrt (52), or approximately 7.21 units.
Advertisement
Calculator, Practice Problems, and Answers
Community Q&A
Search
-
QuestionHow do I find the horizontal distance between (3, 4) and (8, 4)?Community AnswerSubtract 3 from 8 since both are at 4 on the y axis. So distance is: 8-3=5.
-
QuestionWhat is the distance from the x-axis to (7,-2)?Community AnswerThis is an ambiguous question. I will assume you mean the shortest distance. Then, your second point will be (7,0) because the line that goes through (7,0) and (7,-2) is perpendicular to the x-axis. So your answer is 2.
-
QuestionWhat is the distance between (2, 3) and (-8,12)?Community AnswerUsing the distance formula shown in the above article, find the horizontal distance between the two points by subtracting (-8) from 2, which is 10. Then find the vertical distance between the points by subtracting 12 from 3, which is -9. We then add together the squares of those two distances: 3² + (-9)² = 9 + 81 = 90. Find the square root of that sum: √90 = 9.49. That's the distance (in "units") between the two points.
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
Advertisement
Video
Tips
- It doesn't matter if you get a negative number after subtracting y2 - y1 or x2 - x1. Because the difference is then squared, you will always get a positive distance in your answer. [5] X Research sourceThanks
Submit a Tip
All tip submissions are carefully reviewed before being published
Name
Please provide your name and last initial
Thanks for submitting a tip for review!
Advertisement
References
- ↑ http://www.purplemath.com/modules/distform.htm
- ↑ http://mathsfirst.massey.ac.nz/Algebra/PythagorasTheorem/pythapp.htm
- ↑ http://www.mathwarehouse.com/algebra/distance_formula/index.php
- ↑ https://www.mathsisfun.com/algebra/distance-2-points.html
- ↑ https://www.skillsyouneed.com/num/positive-negative.html
About This Article
Article Summary
X
To find the distance between two points on a line, take the coordinates of the two points. Label one as Point 1, with the coordinates x1 and y1, and label the other Point 2, with the coordinates x2 and y2. Plug these values into the distance formula, which is the square of X2 minus X1 plus the square of Y2 minus Y1, then the square root of that result. To see the distance formula written out, read on!
Did this summary help you?
Thanks to all authors for creating a page that has been read 1,017,779 times.
Reader Success Stories
- "Thank you so much! I was literally crying in frustration because I didn't understand it, and my teacher, although very nice, doesn't speak the English language as her first language. I can say with pride that I'm now crying with happiness for success!" ..." more
Advertisement