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प्रश्न
Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
पर्याय
True
False
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उत्तर
This statement is False.
Explanation:
Now, distance between A(4, 3) and B(6, 4),
AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`
AB = `sqrt((6 - 4)^2 + (4 - 3)^2`
= `sqrt(2^2 + 1^2)`
= `sqrt(5)`
Distance between B(6, 4) and C(5, – 6),
BC = `sqrt((5 - 6)^2 + (-6 - 4)^2`
= `sqrt((-1)^2 + (-10)^2`
= `sqrt(1 + 100)`
= `sqrt(101)`
Distance between C(5, – 6) and D(– 3, 5),
CD = `sqrt((-3 - 5)^2 + (5 + 6)^2`
= `sqrt((-8)^2 + (11)^2`
= `sqrt(64 + 121)`
= `sqrt(185)`
Distance between D(– 3, 5) and A(4, 3),
DA = `sqrt((4 + 3)^2 + (3 - 5)^2`
= `sqrt(7^2 + (-2)^2`
= `sqrt(49 + 4)`
= `sqrt(53)`
In parallelogram, opposite sides are equal.
Here, we see that all sides AB, BC, CD and DA are different.
Hence, given vertices are not the vertices of a parallelogram.
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
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