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?

Solution (By Examveda Team)

Slope (m₁) of line which passes through two points (-3, 4) and (0, 3)
$$\eqalign{ & {m_1} = \left( {\frac{{3 - 4}}{{0 + 3}}} \right)\,\,\,\,\,\left[ {\because m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}} \right] \cr & \Rightarrow {m_1} = \frac{{ - 1}}{3} \cr} $$
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,
$$\eqalign{ & \therefore {m_1} \times {m_2} = - 1 \cr & \frac{{ - 1}}{3} \times \left[ { - \left( {x - 7} \right)} \right] = - 1 \cr & x - 7 = - 3 \cr & x = 4 \cr} $$