Find Distance Between Two Points

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To find the distance between two points whose co-ordinates are given. Let P1 and P2 are the two given points, and let their co-ordinates are respectively (x1 y1) and (x2 y2). Therefore, by trigonometry we can find that the distance between two points is given by the formula

The distance P1 P2 =  Ö [(x1 – x2)2 + (y1 – y2)2]

Note : The distance of the point (x1, y1) from the origin is Ö(x12 + y12) because the coordinates of the origin are (0, 0). The axes are rectangular.

Example1 : Let us find the distance between the pairs of points (2, 3) and (5, 7).

Solution : We have to find the distance between the pairs of points (2, 3) and (5, 7).
Let x1 = 2,   y1 = 3 and x2 = 5,   y2 = 7 

Hence required distance
= Ö (x1 – x2)2 + (y1 – y2)2
= Ö (2 - 5)2 + (3 – 7)2
= Ö (-3)2 + (-4)2     = Ö 9 + 16 = Ö25   = 5   

The distance between two points = 5

Example 2. Find the distance between the pairs of points (-3,-2) and (-6, 7)
                    The axes are being inclined at 600.
Let x1 = -3,   y1 = -2 and x2 = -6,   y2 = 7 and q = 600 

Hence required distance
= Ö (x1 – x2)2 + (y1 – y2)2 +2 (x1 – x2) (y1 – y2) Cos q
= Ö (-3 + 6)2 + (-2-7)2 +2(-3+6) (-2-7) Cos 600
= Ö (3)2 + (-9)2 + 2 (3) (-9). 1/2

The distance = Ö 9 + 81 - 27 = Ö63 = 3Ö7.

 
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