For triangle PQR, find equation of altitude PS if co-ordinates of P, Q and R are (1, 2), (2, -1) and (0,5) respectively?

Solution (By Examveda Team)

Given,
P(1, 2), Q(2, -1) and R(0, 5)
Slope of line QR (m₁) $$ = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{5 - \left( { - 1} \right)}}{{0 - 2}} = - 3$$
If the lines are perpendicular then product of slopes is equal to -1
m₁ × m₂ = -1
-3 × m₂ = -1
m₂ = $$\frac{1}{3}$$
∴ Equation of line passes through the point (1, 2) whose slope (m₂) = $$\frac{1}{3}$$
y - y₁ = m₂(x - x₁)
y - 2 = $$\frac{1}{3}$$(x - 1)
y - $$\frac{1}{3}$$x = 2 - $$\frac{1}{3}$$
3y - x = $$\frac{5}{3}$$ × 3
x - 3y = -5