CK-12 Geometry-Concepts

3.10. Distance Formula in the Coordinate Plane http://www.ck12.org

3.10 Distance Formula in the Coordinate Plane

Here you’ll learn the Distance Formula and you’ll use it to find the distance between two points.

What if you were given the coordinates of two points? How could you find how far apart these two points are? After
completing this Concept, you’ll be able to find the distance between two points in the coordinate plane using the
Distance Formula.

Watch This

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CK-12 Foundation: Chapter3DistanceFormulaintheCoordinatePlaneA

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James Sousa: The Distance Formula

Guidance

The shortest distance between two points is a straight line. This distance can be calculated by using the distance

formula. The distance between two points(x 1 ,y 1 )and(x 2 ,y 2 )can be defined asd=

√

(x 2 −x 1 )^2 +(y 2 −y 1 )^2.
Let’s extend this concept to the shortest distance between a point and a line.

Just by looking at a few line segments fromAto linel, we can tell that the shortest distance between a point and a
line is theperpendicular linebetween them. Therefore,ADis the shortest distance betweenAand linel.