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The Pythagorean theorem defines Euclidean distance between two points in space.
If the coordinates of A are (xa, ya, za) and those of B are (xb, yb, zb) then, using the Pythagoras theorem in 3-dimensions,
|AB| = sqrt[(xa - xb)2 + (ya - yb)2 + (za - zb)2]
However, Euclidean distance is not the only distance metric. A simple example of a non-Euclidean metric is the metric variously known as the Taxicab, Manhattan or Minkowski metric. This is based on a grid of mutually perpendicular lines and the distance between two points A = (p, q) and B = (r, s) is (r-p) + (s-q). To go from A to B on the grid of streets and avenues in [downtown] Manhattan, the cab has to go travel (r-p) units in one direction and (s-q) in an orthogonal direction.
There are many other possible metrics. So, the Pythagorean theorem is only one of many possible formulae for distance.
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Is The Distance Formula is derived from the Pythagorean Theorem?
No.
What formula is used to find the length between two points in a coordinate plane?
It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]
Which formula can be derived by using the Pythagorean theorem in the coordinate plane?
The Pythagorean theorem, which is the square root of the sum of the squares of two sides of a right triangle is equal to the hypotenuse, can be used to find the distance between two points. This means that it can also be used to find the equation of a line.
To find the distance between any two points in the planes do you distance formula?
Yes
Converse of Pythagorean Theorem?
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
