First slide

Equation of line in Straight lines

Question

A point R on the x-axis such that PR+RQ is minimum when P= (1, 1) and Q= (3, 2) is

NA

A

$(- \frac{5}{2}, 0)$
B

$(\frac{5}{2}, 0)$
C

$(\frac{5}{3}, 0)$
D

$(- \frac{5}{3}, 0)$

Solution

Since P and Q lie on the same side of x-axis the image of Q(3,2) about x-axis is $Q' (3, - 2)$
$then the equation of the line {PQ}^{1} is y - 1 = \frac{- 2 - 1}{3 - 1} (x - 1)$
$\Rightarrow 3 x + 2 y - 5 = 0$
$This line meets x -axis at R (\frac{5}{3}, 0)$

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