For triangle PQR, find equation of altitude PS if co­ordinates of P, Q and R are (6,2), (0,3) and (­4,5) respectively?

Coordinates of P(6,2) , Q(0,3) and R(4,5). PS is perpendicular to QR

Slope of line QR = $$\frac{5 - 3}{4 - 0} = \frac{1}{2}$$

Product of slopes of two perpendicular lines = -1

Let slope of line PS = $$m$$

=> $$m \times \frac{1}{2} = -1$$

=> $$m = -2$$

Now, equation of line having slope $$m$$ and passing through $$(x_1 , y_1)$$ is $$(y - y_1) = m(x - x_1)$$

=> $$(y - 2) = -2 (x - 6)$$

=> $$y - 2 = -2x + 12$$

=> $$2x + y = 12 + 2 = 14$$

=> Ans - (D)