Linear Inequalities

Question
CBSEENMA11015509

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

  • 29/5

  • 5

  • 6

  • 11/5

Solution

C.

6

Line L : 2x +y = k passes through the point (say P) which divides a lie segment (say AB) in ratio 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
straight p space open parentheses fraction numerator 3 space straight x 2 plus 2 space straight x 1 over denominator 3 plus 2 end fraction comma fraction numerator space 3 straight x space 4 plus 2 straight x 1 over denominator 3 plus 2 end fraction close parentheses space equals space straight P open parentheses 8 over 5 comma 14 over 5 close parentheses
Also, since the line L passes through P, hence substituting the coordinates of straight P space open parentheses 8 over 5 comma 14 over 5 close parentheses  in the equation of line L: 2x +y = k, 
we get
2 space open parentheses 8 over 5 close parentheses plus open parentheses 14 over 5 close parentheses space
rightwards double arrow space straight k space equals space 6

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