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Distance between two points

To find the distance between two points (in a 2D plane) we can use the pythagorean theorem:

Formula for distance between two points

Section titled “Formula for distance between two points”

We can derive this, however, by considering to be the difference in the -coordinates of the two points, to be the difference in the -coordinates of the two points, and to be the distance between the two points:

Rearranging this to make the subject gives us the formula for the distance between two points:

Find the distance between the points (3, 4) and (7, 1).

Section titled “Find the distance between the points (3, 4) and (7, 1).”
  • Values we know:
  • Substitute into the formula:
  • Answer: The distance between the points (3, 4) and (7, 1) is 5 units.

Find the distance between the points (-2, 5) and (4, -1).

Section titled “Find the distance between the points (-2, 5) and (4, -1).”
  • Values we know:
  • Substitute into the formula:
  • Answer: The distance between the points (-2, 5) and (4, -1) is units.