First slide

Equation of line in Straight lines

Question

Let $P Q R$ be a right angled isosceles triangle right angled at $P$ (2, 1). If the equation of the line $Q R$ is $2 x + y = 3$ , then the equations representing the pair of lines $P Q$ and $P R$ is

Moderate

A

$x + 3 y = 5, 3 x - y = 5$
B

$x + y = 3, x - y = 1$
C

$2 x + 3 y = 7, 3 x - 2 y = 4$
D

$3 x + y = 7, x - 3 y = - 1$

Solution

Let the slopes of $P Q$ and $P R$ be $m and - 1 / m$ respectively. Since $P Q R$ is an isosceles triangle $P Q R =$ $PRQ$
$|\frac{m + 2}{1 - 2 m}| = |\frac{- \frac{1}{m} + 2}{1 + \frac{2}{m}}|$
[∵ slope of QR = – 2]
$\Rightarrow m + 2 = \pm (1 - 2 m) f i m = 3 o r - 1 / 3$
So the equations of $P Q$ and $P R$ are
$(y - 1) = 3 (x - 2) and y - 1 = (- 1 / 3) (x - 2)$

$\Rightarrow 3 x - y = 5, x + 3 y = 5$

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