If a line intercepted between the coordinate axes is trisected at a point A(4,3), which is…

Question

If a line intercepted between the coordinate axes is trisected at a point $A(4,3)$, which is nearer to $x$-axis, then its equation is:

Accepted Answer

$A(4,3)$ divides the segment $CB$ (where $C$ is on $x$-axis, $B$ on $y$-axis) in ratio $2:1$ from $C$ (since it's nearer to $x$-axis, i.e. closer to $C$).

$$4 = \frac{1\times0+2\times a}{3} \implies a=6 \implies C=(6,0)$$
$$3=\frac{1\times b+2\times0}3 \implies b=9 \implies B=(0,9)$$

Line through $(6,0),(0,9)$: slope $=-\dfrac32$: $y=-\dfrac32(x-6) \implies 2y=-3x+18 \implies 3x+2y=18$

Solutions · 1