Online Math Homework Help

Friday, June 11, 2010

distance formula in coordinate geometry

Let us study about distance formula in coordinate geometry,

In Figure, A is (2, 2), B is (5, 2), and C is (5, 6)


Finding the distance from A to C.



To find AB or BC, only simple subtracting is necessary.

AB = 5 − 2

and

BC = 6 − 2

AB = 3


BC = 4

To find AC, though, simply subtracting is not sufficient. Triangle ABC is a right triangle with AC the hypotenuse. Therefore, by the Pythagorean Theorem,




If A is represented by the ordered pair ( x1, y1) and C is represented by the ordered pair ( x2, y2), then AB = ( x2 − x1) and BC = ( y2 − y1).

Then




This is stated as a theorem.

Theorem: If the coordinates of two points are ( x1, y1) and ( x2, y2), then the distance, d, between the two points is given by the following formula (Distance Formula).




Example 1: Use the Distance Formula to find the distance between the points with coordinates (−3, 4) and (5, 2).





Example 2: A triangle has vertices A(12,5), B(5,3), and C(12, 1). Show that the triangle is isosceles.

By the Distance Formula,




Because AB = BC, triangle ABC is isosceles.

Hope the above explanation helped you.
Posted by Unknown at 4:37 PM
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