Let two points be mathrm{A}(1,-1) and mathrm{B}(0,2) . If a point mathrm{P}left(mathrm{x}^{prime}, m

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9.Straight Line

hard

Let two points be $\mathrm{A}(1,-1)$ and $\mathrm{B}(0,2) .$ If a point $\mathrm{P}\left(\mathrm{x}^{\prime}, \mathrm{y}^{\prime}\right)$ be such that the area of $\Delta \mathrm{PAB}=5\; \mathrm{sq}$ units and it lies on the line, $3 x+y-4 \lambda=0$ then a value of $\lambda$ is

A

$1$

B

$4$

C

$3$

D

$-3$

(JEE MAIN-2020)

Solution

$\overline{A B}: 3 x+y-2=0$

Also, $\frac{1}{2} \times \sqrt{10} \times h=5$

$\Rightarrow h=\sqrt{10}$

$\Rightarrow \frac{|4 \lambda-2|}{\sqrt{10}}=\sqrt{10} \Rightarrow \lambda=3,-2$

Standard 11

Mathematics

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