The Distance Formula
You know that the distance between two points in a plane with Cartesian coordinates and is given by the following formula:
The distance formula is really just the Pythagorean Theorem in disguise.
To calculate the distance between point and , first draw a right triangle which has the segment as its hypotenuse.
If the lengths of the sides are and , then by the Pythagorean Theorem,
Solving for the distance , we have:
Since is a horizontal distance, it is just the difference between the -coordinates: . Similarly, is the vertical distance .
Since we're squaring these distances anyway (and squares are always non-negative), we don't need to worry about those absolute value signs.
Find the distance between points and in the figure above.
In the above example, we have:
or approximately units.