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प्रश्न
Prove that the points P (0, -4), Q (6, 2), R (3, 5) and S (-3, -1) are the vertices of a rectangle PQRS.
उत्तर
PQ = `sqrt((6 - 0)^2 + (2 + 4)^2) = 6sqrt(2)"units"`
QR = `sqrt((6 -3)^2 + (2 - 5)^2) = 3sqrt(2)"units"`
RS = `sqrt((3 +3)^2 + (5 + 1)^2) = 6sqrt(2)"units"`
PS = `sqrt((-3 - 0)^2 + (-1 + 4)^2) = 3sqrt(2)"units"`
PR = `sqrt((3 - 0)^2 + (5 + 4)^2) = 3sqrt(10)"units"`
QS = `sqrt((6 +3)^2 + (2 + 1)^2) = 3sqrt(10)"units"`
∵ PQ = RS and QR = PS,
Also PR = QS
∴ PQRS is a rectangle.
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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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