The line passing through (-3, 4) and (0, 3) is perpendicular to the line passing through (5, 7) and (4, x). What is the value of x?

Answer: Option A

Slope (m₁) of line which passes through two points (-3, 4) and (0, 3)
$$\begin{array}{rl}& m_1=\left(\frac{3-4}{0+3}\right)\left[\because m=\frac{y_2-y_1}{x_2-x_1}\right]\\ & \Rightarrow m_1=\frac{-1}{3}\end{array}$$
Similarly, slope (m₂) of line which passes through the two points (5, 7) and (4, x)
$$m_2=\frac{x-7}{4-5}=-\left(x-7\right)$$
∵ These lines perpendicular to each other,
$$\begin{array}{rl}& \therefore m_1\times m_2=-1\\ & \frac{-1}{3}\times \left[-\left(x-7\right)\right]=-1\\ & x-7=-3\\ & x=4\end{array}$$