Let P be (5, 3) and a point R on y = x and Q on the x-axis be such that PQ + QR + RP is minimum. Then the coordinates of Q are

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Let $P$ be $(5, 3)$ and a point R on $y = x$ and Q on the x-axis be such that $P Q + Q R + R P$ is minimum. Then the coordinates of $Q$ are

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none of these

(17/4,0)

(17/2,0)

(17,0)

answer is A.

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Detailed Solution

P' and P'' are the images of P w.r.t y = x and y = 0, respectively.

Therefore, $P ’ = (5, 3)$ . The equation of P'P'' is

$y + 3 = \frac{5 + 3}{3 - 5} (x - 5)$

$∴ x = 5 + 3 (- \frac{1}{4}) = \frac{17}{4}$

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