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9.4 Distances and Distance Formula

With the help of x and y axis we saw how the position of a point in the co-ordinate plane was determined. We shall now extend this theory to calculate the distances between any two points in the co-ordinate plane.

Let A (x, y) and B (x2, y2) be two points in the co-orrdinate plane as shown below :

Figure 9.4

In order to find the distance between points A and B we go through following steps and use the distance formula.

Step 1 Draw a line parallel to x-axis through the point A and
           draw a line parallel to y-axis through point B such that
           they intersect at point C.

Step 2 We now have a right triangle with seg AB as the
           hypotenuse. Therefore, by Pythagorean theorem,

            (AB)2 = (AC)2 + (BC)2

            \ AB =

Step 3 The co-ordinates of point C can be determined
           as (x2, y1).

Step 4 The distance between A and C is,

            AC = (x2, x1)

            \ (AC)2 = (x2, x1)2        and

            The distance between B & C is

            BC = (y2, y1)

            \ (BC)2 = (y2, y1)2

Step 5 Substituting the values of (AC)2 and (BC)2 in
            eg (1) we get

               

             This is the distance formula.

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Index

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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