Question

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 – 2y = 4. If the particles move towards increasing y, then their new positions are

• A. (2 -√2, √2 –1), (2√5 +2, √5 –1)
• B. (2√5 + 2, √5 – 1), (2 +√2, √2 +1)
• C. (2+√2, √2 + 1), (2√5 +2, √5 +1)
• D. None of these

Answer 1

Answer: (A)

(2 -√2, √2 –1), (2√5 +2, √5 –1)

Answer 2

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 = tan135°.

Slope of PB = 1/2 = tanθ

⇒ sinθ = .

The coordinates of B

i.e. (x₁ + rcosθ, y₁ + rsinθ) are (2√5 + 2, √5 – 1).

The coordinates of A i.e. (x₁ + rcos135⁰, y₁ + rsin135⁰) are (2- √2, √2-1)