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Mathematics

Assertion (A): The distance between the point A(x, 2x) and point B(x, 0) is 4 units, then point B = (2, 0).

Reason (R):

(x−x)2+(2x−0)2\sqrt{(x - x)^2 + (2x - 0)^2} = 4
⇒ x2 = 4 and x = ± 2
∴ B = (2, 0) or (-2, 0)

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Distance Formula

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Answer

A is false, R is true.

Explanation

Let (x1, y1) = (x, 2x) and (x2, y2) = (x, 0).

The distance between the point A(x, 2x) and point B(x, 0) is 4 units.

⇒ (x−x)2+(0−2x)2\sqrt{(x - x)^2 + (0 - 2x)^2} = 4

⇒ 02 + (- 2x)2 = 42

⇒ 4x2 = 16

⇒ x2 = 164\dfrac{16}{4}

⇒ x2 = 4

⇒ x = 4\sqrt{4}

⇒ x = + 2 or -2

So, B = (2, 0) or (-2, 0)

According to Assertion, B = (2, 0)

∴ Assertion (A) is false.

From above calculations, B = (2, 0) or (-2, 0)

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.

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