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Theorem 1 :
If the co-ordinates of two points are (x1, y1) and (x2, y2), then the distance d between them is given by the formula :

Example 1

Using the distance formula determine the distance between the points with co-ordinates ( 4, -2 ) and (6, 3 ).

Solution :

Let (4, -2) be (x1, y1) and

(6, 3) be (x2, y2). Then according to the distance formula,

Example 2

A triangle has vertices A (2,2), B (5,2) and C (5,6). Show that the triangle is a right angled triangle.

Solution :

By the distance formula

\ d(AC) = 5, d (AB) = 3, and d (BC) = 4

According to Pythagorean if the sum of the square of two sides are equal to the square of the third side then the triangle is a right angled triangle.

Therefore, the triangle is right angled triangle.

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9.1 Points And Co-ordinates
9. 2 Co-ordinates and Axes
9. 3 Quadrants
9. 4 Distances And Distances Formula
9. 5 Mid Point Formula
9. 6 Slope Of A Line
9. 7 Equation Of A Line

Chapter 1

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