3
algebra

Which system defines a square of side length 2 centered at the origin?

A

∣x∣≤1,∣y∣≤1|x| \leq 1, |y| \leq 1

B

∣x∣≤2,∣y∣≤2|x| \leq 2, |y| \leq 2

C

x2+y2≤4x^2 + y^2 \leq 4

D

∣x∣+∣y∣≤1|x| + |y| \leq 1

Correct Answer: A

Choice A is the correct answer. Analyze boundaries.

  1. Side length 2: Means extending 1 unit from center in each direction.
  2. X-bounds: −1≤x≤1→∣x∣≤1-1 \leq x \leq 1 \rightarrow |x| \leq 1
  3. Y-bounds: −1≤y≤1→∣y∣≤1-1 \leq y \leq 1 \rightarrow |y| \leq 1

?�� Strategic Tip:∣x∣≤a|x| \leq a creates a vertical strip width 2a2a. ∣y∣≤a|y| \leq a creates a horizontal strip.

Choice B is incorrect because side length is 4. Choice C is incorrect because it is a circle. Choice D is incorrect because it is a diamond (rotated square).

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Linear Functions Set 79