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Set 6: Linear Inequalities

Explanation

Answer: A

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

A.

∣x∣≤1,∣y∣≤1|x| \leq 1, |y| \leq 1

✓ Correct
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

Detailed Explanation

Choice A is correct. 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).

Key Steps:

•

The correct answer is ∣x∣≤1,∣y∣≤1|x| \leq 1, |y| \leq 1

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.
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