# Distance Formula

The distance formula is derived by using the Pythagorean theorem.Notice in the figure below that the distance between the points (

Applying the Pythagorean theorem yields
*x*,*y*) and (*a*,*b*) is the hypotenuse of a right triangle. The difference*y â€“ b*is the measure of the height of the triangle, and the difference*x â€“ a*is the length of base of the triangle.â€‹

Taking the square root of both sides this equation yields

â€‹

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Example

*In the figure, the circle is centered at the origin and passes through point P. Which one of the following points does it also pass through?*

*(3, 3)**(2, 6)**(â€“3, 4)*

Solution

Since the circle is centered at the origin and passes through the point (0, â€“3), the radius of the circle is 3.

Now, if any other point is on the circle, the distance from that point to the center of the circle (the radius) must also be 3. Look at choice (B).
Using the distance formula to calculate the distance between and (0, 0) (the origin) yields

Hence, is on the circle, and the answer is (B).