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

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

none of these


Answers (1)

best_answer

P(2, –1) goes 2 units along x + y = 1 upto A and 5 units along
x – 2y = 4 upto B.
slope of PA = – 1 = \tan 135^{\circ}
slope of PB = =1 / 2=\tan \theta
\Rightarrow \quad \sin \theta=\frac{1}{\sqrt{5}}, \cos \theta=\frac{2}{\sqrt{5}}
The coordinates of B 
\text { i.e. }\left(x_1+r \cos \theta, y_1+r \sin \theta\right) \text { are }(2 \sqrt{5}+2, \sqrt{5}-1)
The coordinates of A \text { i.e. }\left(x_1+r \cos 135^{\circ}, y_1+r \sin 135^{\circ}\right) \text { are }(2-\sqrt{2}, \sqrt{2}-1)

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