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प्रश्न
Name the type of quadrilateral formed, if any, by the following point, and give reasons for your answer:
(−3, 5), (3, 1), (0, 3), (−1, −4)
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उत्तर
Let the points (−3, 5), (3, 1), (0, 3), and (−1, −4) be representing the vertices A, B, C, and D of the given quadrilateral respectively.
AB = `sqrt((-3,-3)^2 + (5-1)^2)`
= `sqrt((-6)^2+(4)^2)`
= `sqrt(36+16)`
= `sqrt(52)`
= `2sqrt13`
BC = `sqrt((3-0)^2+(1-3)^2)`
= `sqrt((3)^2+(-2)^2)`
= `sqrt(9+4)`
= `sqrt13`
CD = `sqrt((0-(-1))^2+(3-(-4))^2)`
= `sqrt((1)^2+(7)^2)`
= `sqrt(1+49)`
= `sqrt50`
= `5sqrt2`
AD = `sqrt((-3-(-1))^2+(5-(-4))^2)`
= `sqrt((-2)^2+ (9)^2)`
= `sqrt(4+81)`
= `sqrt85`
AC = `sqrt ([0 - (-3)^2] + (3 - 5)^2)`
= `sqrt ((3)^2 + (-2)^2)`
= `sqrt (9 + 4)`
= `sqrt13`
BD = `sqrt ((-1 - 3)^2 + (-4 - 1)^1)`
= `sqrt ((-4)^2 + (5)^2)`
= `sqrt (16 + 25)`
= `sqrt41`
It can be observed that all sides of this quadrilateral are of different lengths. Therefore, it can be said that it is only a general quadrilateral, and not specific such as square, rectangle, etc.
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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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[or]
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