Question

A straight line cuts the coordinate axes at $A$ and $B$. If the midpoint of $AB$ is $(3,2)$, then find the equation of $AB$.

• A. $2x+3y-12=0$
• B. $2x+3y+12=0$
• C. $2x+3y-24=0$
• D. None of these

Answer 1

Answer: (A)

$2x+3y-12=0$

Let $x-intercept$ be $a$

$y-intercept$ be $b$

The coordinate of $A$ is $(a,0)$ and coordinate of $B$ is $(0,b)$

Midpoint of $AB=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})$

$(3,2)=(\frac{a+0}{2},\frac{0+b}{2})$

by comparing them

$3=\frac{a}{2}2=\frac{b}{2}$

$a=6b=4$

Intercept form of line :

$\frac{x}{a}+\frac{y}{b}=1$

$\frac{x}{6}+\frac{y}{4}=1$

$\frac{2x+3y}{12}=1$

$2x+3y=12$

$2x+3y-12=0$

Hence, this is the answer.