Question

A straight line through the point $A(3,4)$ is such that its intercept between the axes is bisected at $A$. Its equation is

• A. $x+y=7$
• B. $3x–4y+7=0$
• C. $4x+3y=24$
• D. $3x+4y=25$

Answer 1

The correct option is C

$4x+3y=24$

Explanation for the correct answer:

Step 1: Finding the coordinates $\mathit{a}$ and $\mathit{b}$.

Let $P(a,0)$ be the point on the x-axis and $Q(0,b)$ be the point on the y-axis.

Let $A(3,4)$ be the mid point of the line joining $PQ$.

The mid point of $PQ$ is given as,

$$\begin{gathered} \Rightarrow 3=\frac{a+0}{2} \\ a=6 \end{gathered}$$

$$\begin{gathered} \Rightarrow 4=\frac{0+b}{2} \\ b=8 \end{gathered}$$

Step 2: Finding the slope.

The slope m is, $m=\frac{y_2-y_1}{x_2-x_1}$

The slope of the line $P(6,0)andQ(0,8)$ is

$$\begin{gathered} \Rightarrow m=\frac{8-0}{0-6} \\ =-\frac{4}{3} \end{gathered}$$

The equation of straight line with slope is given as, $y-y_1=m(x-x_1)$

The line is passing through the point $P(6,0)$ is

$$\begin{gathered} \Rightarrow y-0=-\frac{4}{3}(x-6) \\ y=\frac{-4x+24}{3} \\ 3y+4x=24 \end{gathered}$$

Hence, option (C) $\mathbf{4}\mathit{x}\mathbf{+}\mathbf{3}\mathit{y}\mathbf{=}\mathbf{24}$ is the correct answer.