Distance formula

Jun 17, 2020, 16:45 IST

Distance formula

Definition and formula description :-
The distance formula is derived from the Pythagorean theorem. To find distance between two points (x1, y1) and (x2, y2), all that you need to do is use the coordinates of these ordered pairs and apply the formula pictured below
The distance formula is

Application in real life :-The distance formula comes with some uses in everyday life. It can be used as a strategy for easy navigation and distance estimation. For example, if you want to estimate the distance of two places on a map, simply get the coordinate of the two places and apply the formula. Or when a pilot wants to know the distance of an incoming plane and his plane, he can use the plane radar and find the coordinates of the two planes and then apply the formula.

Example 1 :-Find the radius of a circle, given that the center is at (2, –3) and the point (–1, –2) lies on the circle.

Solution :-
The radius is the distance between center and any point on the circle, so I need to find the distance:

Example 2 :-Find all points (4, y) that are 10 units from the point (–2, –1).

Solution :-
I’ll plug the two points and the distance into the Distance Formula:

Now I’ll square both sides, so I can get to the variable:
This means y = –9 or y = 7, so:
The two points are (4, –9) and (4, 7).