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Problems Based on Distance Formula
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Coordinate Geometry: Problems Based on Distance Formula
Example 1: Find the value of x, if the distance between the points (x, -2) and (4, 2) is 5.
Solution: Let P (x, -2) and Q (4, 2) be the given points. Then,
PQ = 5 ... [Given]
[(x - 3)2 + (-2 -2)2] = 5
(x - 3) = 5 or (x - 3) = -5
x = 8 or x = -2
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Example 2: Find the value of x, if the distance between the points (x, -1) and (3, 2) is 5.
Solution: Let P (x, -1) and Q (4, 2) be the given points. Then,
PQ = 5 ...[Given]
[(x - 3)2 + (-1 - 2)2] = 5
(x - 3)2 + 9 = 52
x2 - 6x + 18 = 25
x2 - 6x - 7 = 0
(x - 7) (x + 1) = 0
x = 7 or x = -1
 
   
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