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Question
P and Q are two points lying on the x - axis and the y-axis respectively . Find the coordinates of P and Q if the difference between the abscissa of P and the ordinates of Q is 1 and PQ is 5 units.
Solution
P lies on x-axis and Q lies on y-axis
Let abscissa P be x then ordinate of Q is x - 1
∴ P(x , 0) , Q (0 , x - 1)
Given PQ = 5 units
`sqrt (("x" - 0)^2 + (0 - x + 1)^2) = 5`
squaring both sides
x2 + x2 + 1 - 2x = 25
2x2 - 2x - 24 = 0
x2 - x - 12 = 0
x2 - 4x + 3x - 12 = 0
(x - 4)(x + 3) = 0
x = + 4 or - 3
Coordinates of P are (4,0) or (-3,0)
Coordinates of Q are (0,3) or (0,-4)
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