Find Distance Between Two Points

Find Distance Between Two Points 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 = [(x1 x2)2 + (y1 y2)2] Note :The distance of the point (x1, y1) from the origin is (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 = (x1 x2)2 + (y1 y2)2 = (2 - 5)2 + (3 7)2 = (-3)2 + (-4)2 = 9 + 16 = 25 = 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 = (x1 x2)2 + (y1 y2)2 +2 (x1 x2) (y1 y2) Cos q = (-3 + 6)2 + (-2-7)2 +2(-3+6) (-2-7) Cos 600 = (3)2 + (-9)2 + 2 (3) (-9). 1/2 The distance = 9 + 81 - 27 = 63 = 37.