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Find the value of k if the points (2,3) , (5,k) and (6,7) are collinear .A. k = 4B. k = 6C. `k = (-3)/(2)`D. `k = (11)/(4)` |
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Answer» Correct Answer - B Here, `(x_(1) = 2, y_(1) = 3), (x_(2) = 5, y_(2) = k) "and" (x_(3) = 6, y_(3) = 7)` Since the given points are collinear, we must have : `x_(1) (y_(2) - y_(3)) +x_(2)(y_(3)-y_(1)) + x_(3)(y_(1) -y_(2)) = 0` `rArr 2(k-7) + 5(7-3) +6(3-k) = 0 rArr 2k -14 + 20 +18 - 6k = 0` `rArr 4k = 24 rArr k = 6.` |
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