Question

The equation of line whose midpoint is $(x_1,y_1)$ in between the axes is:

• A. $\frac{x}{x_1}+\frac{y}{y_1}=2$
• B. $\frac{x}{x_1}+\frac{y}{y_1}=\frac{1}{2}$
• C. $\frac{x}{x_1}+\frac{y}{y_1}=1$
• D. None of these

Answer 1

The correct option is A

$\frac{x}{x_1}+\frac{y}{y_1}=2$

Explanation for the correct answer:

Finding the equation of line,

Given that the midpoint of the line is $(x_1,y_1)$.

This means that the x-intercept is $=2x_1$

The y-intercept is $=2y_1$

Therefore, the equation of the line in intercept form is:

$\begin{array}{rcl}\frac{x}{a}+\frac{y}{b}& =& 1\\ & \Rightarrow & \frac{x}{2x_1}+\frac{y}{2y_1}=1\\ & \Rightarrow & \frac{x}{x_1}+\frac{y}{y_1}=2\end{array}$

Hence, the correct answer is Option (A)