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Question
The distance between the points (3, 1) and (0, x) is 5. Find x.
Solution
It is given that the distance between the points A (3, 1) and B (0, x) is 5.
∴ AB = 5
AB2 = 25
(0 - 3)2 + (x - 1)2 = 25
9 + x2 + 1 - 2x = 25
x2 - 2x - 15 = 0
x2 - 5x + 3x - 15 = 0
x(x - 5) + 3(x - 5) = 0
(x - 5)(x + 3) = 0
x = 5, -3
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