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Derived from the pythagorean theorem the distance formula is used to find the distance between any 2 given points.
Distance formula maths coordinate geometry. The distance formula is used to find the distance between any two given points. Using distance formula is much easier than the pythagorean theorem. These points are usually crafted on an x y coordinate plane. Construct a figure to derive distance formula.
The formula is ab x2 x1 y2 y1 let us take a look at how the formula was derived. Coordinate geometry involves the use of algebraic processes in the study of geometric problems and also the geometric interpretation of algebraic equations. Given the two points x1 y1 and x2 y2 the distance d between these points is given by the formula. Draw two lines parallel to both x axis and y axis as shown in the figure through p and q.
Stack exchange network consists of 177 q a communities including stack overflow the largest most trusted online community for developers to learn share their knowledge and build their careers. Ab x2 x1 y2 y1 where points are a x1 y1 and b x2 y2 let us look at how this formula is derived. Use the pythagorean theorem to find the distance between two points on the coordinate plane. D x 2 x 1 2 y 2 y 1 2 it is a distance formula and used to find the distance between any two points in a two dimensional cartesian coordinate system.
Distance x 2 x 1 2 y 2 y 1 2. This use of coordinates was descartes s great contribution to mathematics which revolutionized the study of geometry. D x2 x1 2 y2 y1 2 where d is the distance between the points. By pythagoras theorem we can derive the distance formula.
Since this format always works it can be turned into a formula. Ab x2 x1 2 y2 y1 2 a b x 2 x 1 2 y 2 y 1 2 this is the widely used distance formula to determine the distance between any two points in the coordinate plane. The length of the hypotenuse is the distance between the two points. Now learn how to derive the distance formula in geometry.
Let p x1 y1 and q x2 y2 be the coordinates of two points on the coordinate plane.
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