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Distance between Two Points
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Distance between Two Points
The distance between any two points in the plane is the length of the line segment joining them.
The distance between two points P(x1, y1) and Q(x2, y2) is given by
PQ = [(x2 - x1)2 + (y2 - y1)2]
i.e. PQ = [Difference of abscissa)2 + (Difference of ordinate)2]

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Example: Find a point on the x-axis which is equidistant from the points (5, 4) and (-2, 3).
Solution: Since the required point (say M) is on the x-axis, its ordinate will be zero. Let the abscissa of the point be x.
Therefore, coordinates of the point M are (x, 0).
Let P and Q denote the points (5, 4) and (-2, 3), respectively.
Since we are given that PM = QM, we have
PM2 = QM2
(x - 5)2 + (0 - 4)2 = (x +2)2 + (0 - 3)2
x2 + 25 - 10x + 16 = x2 + 4 + 4x + 9
-14x = -28
x = 2
Thus, the required point is (2, 0).

Example: Find the distance between two cities A and B having coordinates (5, 8) and (10, 14) respectively.
Solution: Given two cities A and B have coordinates (5,8) and (10,14) resp.
Distance between these cities is given by = [(y2-y1)2+(x2-x1)2]
=[61] units.
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