If $P(3,4)$ is the mid-point of a line segment between the axes, then what is the equation of the line?

Concept: - Midpoint of $\left(\mathrm{x}_1, \mathrm{y}_1\right)$ and $\left(\mathrm{x}_2, \mathrm{y}_2\right)=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ - The equation of the line passing through $\left(x_1, y_1\right)$ and $\left(x_2, y_2\right)$ is $\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)$ Calculation: Let the points of line on axes be $(h, 0)$ and $(0, k)$ respectively So, $P(3,4)$ is the mid-point of $(h, 0)$ and $(0, k)$ $\begin{aligned} & \Rightarrow(3,4)=\left(\frac{h+0}{2}, \frac{0+k}{2}\right) \\ & \Rightarrow \mathrm{h}=6 \text { and } \mathrm{k}=8 \end{aligned}$ So, the line passes through the points $(6,0)$ and $(0,8)$ $\Rightarrow$ The equation of the line passing through $(6,0)$ and $(0,8)$ is $\begin{aligned} & (y-0)=\frac{8-0}{0-6}(x-6) \\ & \Rightarrow-6 y=8 x-48 \\ & \Rightarrow 4 x+3 y-24=0 \end{aligned}$