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  • Two particles start from the same point (2,-1) one moving 2 units along the line and the other 5 units alo

Two particles start from the same point (2,-1) one moving 2 units along the line x+y=1 and the other 5 units along x-2 y=4. If the particles move towards increasing y, then their new position will be
 

 

Option: 1

(2-\sqrt{2}, \sqrt{2}-1)


Option: 2

(2 \sqrt{5}+2, \sqrt{5}-1)


Option: 3

(2+\sqrt{2}, \sqrt{2}+1)


Option: 4

(2 \sqrt{5}-2, \sqrt{5}-1)


Answers (1)

best_answer

Let: P(2,-1) goes 2 units along x+y=1 upto A and 5 units along x-2 y=4 upto B
Slope of P A=-1=\tan 135^{\circ}, slope of P A=-1=\tan 135^{\circ}
\begin{aligned} \therefore \quad \sin \theta & =\frac{1}{\sqrt{5}}, \cos \theta=\frac{2}{\sqrt{5}} \\ \therefore \quad A & \equiv\left(x_1+r \cos 135^{\circ}, y_1+r \sin 135^{\circ}\right) \\ & =\left(2+2 \times-\left(\frac{1}{\sqrt{2}}\right),-1+2 \times \frac{1}{\sqrt{2}}\right) \\ & =(2-\sqrt{2}, \sqrt{2}-1) \end{aligned}
 

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Nehul

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