The distance formula is derived from the Pythagorean Theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In the distance formula, which is used to find the distance between two points in a coordinate plane, the coordinates of the two points are used as the lengths of the sides of a right-angled triangle. By applying the Pythagorean Theorem to this triangle, we can see that the square of the distance between the two points (the hypotenuse) is equal to the sum of the squares of the differences in the x-coordinates and the differences in the y-coordinates of the two points.
Therefore, the distance formula (d = √((x2-x1)^2 + (y2-y1)^2)) essentially proves the Pythagorean Theorem in the context of finding distances between points on a plane.
How does the distance formula show the Pythagorean Theorem?
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