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For what value of α + β, the three points (α, β), (5, 0), (0, 5) will be collinear?1. 52. -253. 04. 25 |
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Answer» Correct Answer - Option 1 : 5 Concept: If three points are collinear then the area of the triangle formed from these 3 points will be 0. [as the collinear points lie on the same straight line] Analysis: Area of triangle passing through the points (x, y), (x2, y2) and (x3, y3) is given by: \(A = \frac{1}{2}\left[ {x,\;\left( {{y_2} - {y_3}} \right) + {x_2}\left( {{y_3} - {y_1}} \right) + {x_3}\left( {{y_1} - {y_2}} \right)} \right]\) (x1, y1 = α, β); (x2, y2 = 5, 0); (x3, y3 = 0, 5) ∴ \(A = \frac{1}{2}\left[ {\alpha \left( { - 5} \right) + 5\left( {5 - \beta } \right) + 0} \right]\) -5α + 25 – 5β = 0 α + β = 5 |
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