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 equals - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

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If the line 2 x + 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 equals:

Solution & Step-by-step Explanation

The coordinates of the point P (x, y) dividing (1, 1) and (2, 4) in ratio 3 : 2 are: x = \frac{3 ( 2 ) + 2 ( 1 )}{3 + 2} = \frac{8}{5} y = \frac{3 ( 4 ) + 2 ( 1 )}{3 + 2} = \frac{14}{5} Point P = (\frac{8}{5}, \frac{14}{5}) .Since P lies on 2 x + y = k : 2 (\frac{8}{5}) + \frac{14}{5} = k \frac{16}{5} + \frac{14}{5} = k ⟹ k = \frac{30}{5} = 6

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If the line 2 x + 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 equals:

\frac{29}{5}

5

6

\frac{11}{5}

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