Question 82

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?

Solution

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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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?