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As you can see, the distance formula on the plane is derived from the Pythagorean theorem.
Above formula can be written in the following way for given two points and :
Vertical and horizontal lines
If the line segment is exactly vertical or horizontal, the formula above will still work fine, but there is an easier
way. For a horizontal line, its length is the difference between the x‐coordinates. For a vertical line its length is
the difference between the y‐coordinates.
Distance between the point A (x,y) and the origin
As the one point is origin with coordinate O (0,0) the formula can be simplified to:
Example #1
Q: Find the distance between the point A (3,‐1) and B (‐1,2)
Solution: Substituting values in the equation we'll get
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