Q. Determine the equation of the line the portion of which, intercepted by the axes, is divided by the point (-5,4) in the ratio 1:2.

Soln:

We know that the point (-5,4) divides the line in the ratio m:n = 1:2

Let the line through the point (-5,4) meets x-axis at (x1,y1) = (a,0) and y-xis at (x2,y2) = (0,b)

Using section formula for  internal division, we get,

(x,y) = [(mx2+nx1)/(m+n),(my2+ny1)/(m+n)]

(-5,4) = [(1*0+2*a)/(1+2),(1*b+2*0)/(1+2)]

-5 = 2a/3 and 4 = b/3

a = -15/2 and b = 12

Now, using the equation of straight line in double intercept form i.e.

(x/a) + (y/b) = 1

[x/(-15/2)] + (y/12) = 1

-(2x/15) + (y/12) = 1
(-24x + 15y)/180 = 1
-24x + 15y =180
24x - 15y + 180 = 0
3(8x - 5y + 60) = 0

8x - 5y + 60 = 1 is the required equation of st. line.