For triangle PQR, what is the equation of altitude PS if coordinates of P, Q and R are (5,1), (0,4) and (2,3) respectively?
Coordinates of P(5,1), Q(0,4) and R(2,3)
Slope of QR = $$\frac{3-4}{2-0} = \frac{-1}{2}$$
PS is perpendicular to QR, thus product of their slopes is -1
Let slope of PS = $$m$$
=> $$m \times \frac{-1}{2} = -1$$
=> $$m = 2$$
Now, equation of PS having slope, $$m = 2$$ and passing through P(5,1)
=> $$(y - 1) = 2(x - 5)$$
=> $$y - 1 = 2x - 10$$
=> $$2x - y = 10 - 1 = 9$$
=> Ans - (B)
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