# Choose the correct answer from the given four options. 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

$\begin {array} {1 1} (A)\;2x + 3y = 12 & \quad (B)\;3x + 2y = 12 \\ (C)\;4x – 3y = 6 & \quad (D)\;5x – 2y = 10 \end {array}$

Toolbox:
• The coordinates of the midpoint of the line joining the points $(x_1, y_1)$ and $(x_2, y_2)$ is $\bigg( \large\frac{x_1+x_2}{2}$$, \large\frac{y_1+y_2}{2} \bigg) • Equation of a line in its intercept form is \large\frac{x}{a}$$+\large\frac{y}{b}$$=1 , where a and b are the intercepts in the coordinate axes. Step 1 : It is given that the mid point of a line intercepted between the coordinate axes is (3, 2) Let the equation of the line be \large\frac{x}{a}$$+ \large\frac{y}{b}$$=1 Let the points A be (a,o) and B be (0, b) and p(3, 2) Since p is the mid point of AB \large\frac{a+0}{2}$$=3 \Rightarrow a = 6$ and
$\large\frac{b+0}{2}=2 \Rightarrow b = 4$
$\therefore$ The equation of the line is
$\large\frac{x}{6}$$+ \large\frac{y}{4}$$=1$
$\Rightarrow 2x+3y=12$
Hence 'A' is the correct option.