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

My Attempt: Let the equation of straight line be $$ax+by+c=0$$ It passes through the point $(-5,4)$. $$-5a+4b+c=0$$

pi-π
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  • Personally, I would not write the equation of the line as ax+ by+ c= 0 because multiplying each of a, b, and c by the same number would give a different equation of that form for the same line. Instead, divide through by b and write the equation as y= ax+ c. Since it passes through (-5, 4) we have -5= 4a+ c so that c= -4- 4a and we can write the equation as y= ax- 4- 4a or y= a(x- 4)- 4. The y-intercept is where y= 0= a(x- 4)- 4 so x= (4/a)+ 4 so ((4/a)+ 4, 0). The x-intercept is where x= 0 so y= -4a- 4 or (0, -4a- 4). – user247327 Aug 06 '17 at 12:32

2 Answers2

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Let the equation be $$\dfrac xa+\dfrac yb=1$$

So, $(a,0);(0,b)$ is divided in $1:2$ at $(-5,4)$

i.e., $-5=\dfrac{a\cdot2+0\cdot1}{2+1}$ etc.

lab bhattacharjee
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HINT: make the Ansatz $$y=mx+n$$ since $P(-5,4)$ is situated on the line we have $$y=m(x+5)+4$$ and the intersection Point withe the $x$ axes is $$P_x(-5-\frac{4}{m};0)$$ and the y-axes $$P_y(0;5m+4)$$ Now must $$\frac{P_xP}{PP_y}=\frac{1}{2}$$ can you finish?

Dr. Sonnhard Graubner
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