If the line 2x + y = k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2, then k is equal to

Solution :

Given line L : 2x + y = k passes through point (Say P) which divides the line segment (let AB) in ration 3:2, where A(1, 1) and B(2, 4).

Using section formula, the coordinates of the point P which divides AB internally in the ratio 3:2 are

P(\(3\times 2 + 2\times 1\over 3 + 2\), \(3\times 4 + 2\times 1\over 3 + 2\)) = P(\(8\over 5\), \(14\over 5\))

Also, since the line L passes through P, hence substituting the coordinates of P(\(8\over 5\), \(14\over 5\)) in the equation of L : 2x + y = k, we get

2(\(8\over 5\)) + \(14\over 5\) = k

\(\implies\) k = 6

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