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Mathematics

Assertion (A): If A = (2x, y), B(x, 2y) and AB = 5 unit, then x + y = 5.

Reason (R): (x−2x)2+(2y−y)2\sqrt{(x - 2x)^2 + (2y - y)^2} = 5

⇒ x2 + y2 = 25

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are true, and R is the correct reason for A.

  4. Both A and R are true, and R is the incorrect reason for A.

Distance Formula

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Answer

Given, A = (2x, y), B = (x, 2y).

By distance formula,

Distance between two points = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

Since, AB = 5 unit.

Substituting the values, we get :

⇒5=(x−2x)2+(2y−y)2⇒5=(−x)2+y2⇒52=x2+y2⇒x2+y2=25.\Rightarrow 5 = \sqrt{(x - 2x)^2 + (2y - y)^2}\\[1em] \Rightarrow 5 = \sqrt{(-x)^2 + y^2}\\[1em] \Rightarrow 5^2 = x^2 + y^2\\[1em] \Rightarrow x^2 + y^2 = 25.

∴ A is false, but R is true.

Hence, option 2 is the correct option.

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