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Question
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, What are the coordinates of A?
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Solution
Let the point A be (a, a) B is (1, 3)
Distance AB = 10 ...(Given)
By distance formula `sqrt(("a" - 1)^2 + ("a" - 3)^2` = 10
Simplifying 2a2 – 8a + 10 = 100
a2 – 4a – 45 = 0
(a – 9)(a + 5) = 0
⇒ a = – 5, A = (– 5, – 5)
a = 9, A = (9, 9)
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