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

Co­ordinates of P(1,2), Q(2,1) and R(0,5)

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

PS is perpendicular to QR, thus product of their slopes is -1

Let slope of PS = $$m$$

=> $$m \times (-2) = -1$$

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

Now, equation of PS having slope, $$m = \frac{1}{2}$$ and passing through P(1,2)

=> $$(y - 2) = \frac{1}{2}(x - 1)$$

=> $$2y-4 = x - 1$$

=> $$x - 2y = -4 + 1 = -3$$

=> Ans - (C)