Question

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 :
(a) $\frac{29}{5}$
(b) 5
(c) 6
(d) $\frac{11}{5}$

Answer 1

(c) 6

step wise explanation

Answer 2

Answer:

As segment joining (1, 1) and (2, 4) are in ratio 3:2

Therefore x=[3(2) +2(1) ]/3+2 =8/5

y=[3(4) +2(1)]/3+2 =14/5

As line passes through this points it should satisfy the equation

Substituting this values in 2x+y=k we get 16/5+14/5=k

Therefore k=30/5 =6