Question

If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes is $(3,2)$, then the equation of the line will be:

• A. $2x+3y=12$
• B. $3x+2y=12$
• C. $4x-3y=6$
• D. $5x-2y=10$

Answer 1

The correct option is A

$2x+3y=12$

Explanation for the correct option.

Step 1: Find the coordinate of the axes

Let the line intersects the axes at $A(a,0)$ and $B(0,b)$.

Given that, $C(3,2)$ is the mid-point of $AB$.

$\begin{array}{rcl}3& =& \frac{(a+0)}{2}\\ a& =& 6\end{array}$
And

$$\begin{gathered} 2=\frac{0+b}{2} \\ b=4 \end{gathered}$$
Step 2: Find the equation of the line
Intercept form of the line $AB$:

$\begin{array}{rcl}\frac{x}{a}+\frac{y}{b}& =& 1\\ \frac{x}{6}+\frac{y}{4}& =& 1\\ 2x+3y& =& 12\end{array}$
Hence, option A is correct.