Question

A point 'P' moves in xy plane in such a way that [|x|] + [|y|] = 1, where [.] denotes the greatest integer function. Area of the region representing all possible positions of the point 'P' is equal to

• A. 4 sq. units
• B. 16 sq. units
• C. $2 \sqrt { 2 }$sq. units
• D. 8 sq. union

Answer 1

Answer: (D)

8 sq. union

Answer 2

Clearly [|x|] = 1, [|y|] = 0

⇒ 1 ≤ |x| < 2, 0 ≤ |y| < 1

⇒ x ∈ (−2, −1] ∪ [1, 2), y ∈ (-1, 1) or [|x|] = 0, [|y|] = 1 ⇒ 0 ≤ x < 1.

⇒ x ∈ (-1, 1), y ∈ (-2, -1] ∪ [1, 2)

Area of required region = 4(2 - 1) (1 − (-1)) = 8sq. units