First slide

Equation of line in Straight lines

Question

$Let two points be A (1, - 1) and B (0, 2) . If a point P (x', y') be such that the area of$
$Δ PAB = 5 sq units and it lies on the line 3 x + y - 4 λ = 0, then a value of λ is :$

Moderate

A

4
B

3
C

-3
D

1

Solution

$\begin{array}{l} A r e a = \frac{1}{2} |\begin{matrix} 0 & 2 & 1 \\ 1 & - 1 & 1 \\ x' & y' & 1 \end{matrix}| = 5 \\ \Rightarrow - 2 (1 - x') + (y' + x') = \pm 10 \\ \Rightarrow - 2 + 2 x' + y' + x' = \pm 10 \\ \Rightarrow 3 x' + y' = 12 or 3 x' + y' = - 8 \\ \Rightarrow λ = 3, - 2 \end{array}$

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