# 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

### Similar Questions

Find the distance between the line 12x – 5y + 9 = 0 and the point (2,1)

If p is the length of the perpendicular from the origin to the line $$x\over a$$ + $$y\over b$$ = 1, then prove that $$1\over p^2$$ = $$1\over a^2$$ + $$1\over b^2$$

If $$\lambda x^2 – 10xy + 12y^2 + 5x – 16y – 3$$ = 0 represents a pair of straight lines, then $$\lambda$$ is equal to

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 and 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes, then

If PS is the median of the triangle, with vertices of P(2,2), Q(6,-1) and R(7,3), then equation of the line passing through (1,-1) and parallel to PS is