Pythagorean Theorem
The Pythagorean theorem indicates that given a right triangle, we can obtain the following relation between the sides and the hypotenuse.
To obtain the distance between two points (a, c) and (b, d) in a cartesian coordinate system, the following steps may be used:
- Step 1.
- Draw a right triangle with coordinates (a, c), (b, c), and (b, d)
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- Step 2.
- Find the lengths of the two short sides of triangle.
- Step 3.
- Calculate the distance using Pythagoras formula
Example: Find the distance between the points (1, 2) and (3, 5).
Solution: By filling in the following triangle, we can conclude that
Example: Find the distance between the points (-1, 2) and (3, -2).
Solution: By filling in the following triangle, we can conclude that
You've seen us do it with two points. Now try it yourself! The following link will allow you to see the distance given any two points on the coordinate plane!
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