question_answer

The equation of the line which is such that the portion of line segment intercepted between the coordinate axes is bisected at\[(4,-3),\]is

A)  \[3x+4y=24\]

B)  \[3x-4y=12\]

C)  \[3x-4y=24\]

D)  \[4x-3y=24\]

E)  \[4x-3y=12\]

Correct Answer: C

Solution :

Let the coordinates of point A and B are\[(x,\text{ }0)\]and\[(0,-y)\]. \[\therefore \]  \[\frac{x}{2}=4\Rightarrow x=8\] and     \[-\frac{y}{2}=-3\Rightarrow y=6\] \[\therefore \]Equation of line is                 \[\frac{x}{8}+\frac{y}{-6}=1\] \[\Rightarrow \]               \[3x-4y=24\]