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Question
A point A is at a distance of `sqrt(10)` unit from the point (4, 3). Find the co-ordinates of point A, if its ordinate is twice its abscissa.
Solution
It is given that the coordinates of point A are such that its ordinate is twice its abscissa.
So, let the coordinates of point A be (x, 2x).
We have:
`sqrt((x - 4)^2 + (2x - 3)^2) = sqrt(10)`
(x - 4)2 + (2x - 3)2 = 10
x2 + 16 - 8x + 4x2 + 9 - 12x = 10
5x2 - 20x + 25 = 10
5x2 - 20x = 10 - 25
5x2 - 20x = - 15
5x2 - 20x + 15 = 0
x2 - 4x + 3 = 0
x2 - x - 3x + 3 = 0
x(x - 1) -3(x - 1) = 0
(x - 1)(x - 3) = 0
x = 1, 3
Thus, the co-ordinates of the point A are (1, 2) and (3, 6).
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