Question

If $\left(\frac{3}{2},\frac{5}{2}\right)$ is the midpoint of the line segment intercepted by a line between axes, then the equation of the line is

• A. $5x+3y+15=0$
• B. $3x+5y+15=0$
• C. $5x+3y–15=0$
• D. $3x+5y–15=0$

Answer 1

The correct option is C

$5x+3y–15=0$

Explanation for the correct option:

Find the equation of the line:

Given, $\left(\frac{3}{2},\frac{5}{2}\right)$ is the midpoint of the line segment.

Now, The coordinates of the line segment on x axis will be $(a,0)$ and on y axis will be $(0,b)$.

Mid - point $=\left(\frac{a+0}{2},\frac{0+b}{2}\right)$ $\left[\because Mid-point=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right]$

$\left(\frac{3}{2},\frac{5}{2}\right)=\left(\frac{a}{2},\frac{b}{2}\right)$

So, the $x$ intercept $a=3$ and $y$ intercept, $b=5$.

As we know, Equation of line in intercept form is $\frac{\mathbf{x}}{\mathbf{a}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{y}}{\mathbf{b}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}$

$\Rightarrow$ $\frac{x}{3}+\frac{y}{5}=1$

$\Rightarrow$ $5x+3y=15$

$\Rightarrow$$5x+3y–15=0$

$\therefore$The equation of the line is $\mathbf{5}\mathit{x}\mathbf{}\mathbf{+}\mathbf{}\mathbf{3}\mathit{y}\mathbf{}\mathbf{–}\mathbf{}\mathbf{15}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$

Hence, Option ‘C’ is Correct.