How to Find the Distance Between Two Points Using a Rectangular Coordinate System

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The rectangular coordinate system, also known as the Cartesian coordinate system, identifies points based on their x- and y-coordinates. When you have two points identified by their coordinates, you can find the distance between the two points using the distance formula, which derives from the Pythagorean theorem. You can form a right triangle with the two points and then use the change in the x-coordinates to find one side and the change in the y-coordinates to find the other side. From there, you can calculate to find the hypotenuse, which measures the distance between the two points.

Things You'll Need

  • Calculator
  • Subtract the first x-coordinate from the second x-coordinate. For example, if your coordinates are (-3, 5) and (4, 2), subtract -3 from 4 to get 7.

  • Subtract the first y-coordinate from the second y-coordinate. For example, if your coordinates are (-3, 5) and (4, 2), subtract 5 from 2 to get -3.

  • Square the differences. In this example, square 7 to get 49 and square -3 to get 9.

  • Add the squares. In this example, add 49 and 9 to get 58.

  • Calculate the square root of the Step 4 result to find the distance between the two points. Completing the example, take square root of 58 to find the distance is approximately 7.62.

References

  • Photo Credit Jupiterimages/BananaStock/Getty Images
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