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प्रश्न
Determine whether the point is collinear.
R(0, 3), D(2, 1), S(3, –1)
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उत्तर
R(0, 3), D(2, 1), S(3, –1)
RD = \[\sqrt{\left( 2 - 0 \right)^2 + \left( 1 - 3 \right)^2}\]
= `sqrt((2)^2 + (- 2)^2)`
= `sqrt(4 + 4)`
= `sqrt8`
= `sqrt(4 xx 2)`
= `2sqrt2`
DS = `sqrt((3 - 2)^2 + ((-1) - 1)^2)`
= `sqrt((1)^2 + (-2)^2)`
= `sqrt(1 + 4)`
= `sqrt5`
RS = `sqrt((3 - 0)^2 + ((-1) - 3)^2)`
= `sqrt((3)^2 + (-4)^2)`
\[ = \sqrt{9 + 16}\]
\[ = \sqrt{25}\]
\[ = 5\]
Sum of two sides is not equal to the third side.
Hence, the given points are not collinear.
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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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