CAT 2020 Question Paper | Quants Slot 3

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This question is from Co-ordinate Geometry. Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's - you get Co-ordinate Geometry. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope. CAT exam does test one on ideas from Coordinate Geometry once in a while. It is important to cover ideas from Coordinate Geometry in your CAT Preparation.

Question 25 : The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is

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Video Explanation

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Explanatory Answer

The line x + 9y + c = 0, forms one of the diagonal of the parallelogram.
The other diagonal connects the points (2, 1) and (-3, -4).

The diagonals of a parellogram bisect each other, hence the line x + 9y + c = 0 should pass hrough the midpoint of the line joining (2, 1) and (-3, -4).

The midpoint of the line joining (2, 1) and (-3, -4) = ( \\frac{2-3}{2}) , \\frac{1-4}{2}) ) = ( \\frac{-1}{2}) , \\frac{-3}{2}) ) = (-0.5 , -1.5)
Therefore, the line x + 9y + c = 0 passes through (-0.5 , -1.5),
Hence, (-0.5) + 9(-1.5) + c = 0
(-0.5) + 27(-0.5) + c = 0
28 (-0.5) + c = 0
-14 + c = 0
c = 14.

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The question is "The points (2 , 1) and (-3 , -4) are opposite vertices of a parellelogram. If the other two vertices lie on the line x + 9y + c = 0, then c is"

Hence, the answer is, "14"

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