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प्रश्न
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.
उत्तर
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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Tharunya was thrilled to know that the football tournament is fixed with a monthly timeframe from 20th July to 20th August 2023 and for the first time in the FIFA Women’s World Cup’s history, two nations host in 10 venues. Her father felt that the game can be better understood if the position of players is represented as points on a coordinate plane. |
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