AMC 10B/12B 2023 (Problems 9/13)What is the area of the region in the coordinate plane defined by ∣∣x∣−1∣+∣∣y∣−1∣≤1\left||x|-1\right|+\left||y|-1\right|\le1∣∣x∣−1∣+∣∣y∣−1∣≤1?(A) 2\text{(A)}\;2(A)2(B) 8\text{(B)}\;8(B)8(C) 4\text{(C)}\;4(C)4(D) 15\text{(D)}\;15(D)15(E) 12\text{(E)}\;12(E)12Related TopicsCoreFunction TransformationsAbsolute ValueCheck AnswerYour answer:ABCDECheckHints (4)Hint 1Assume x,y≥0x,y\ge0x,y≥0. Then graph ∣x−1∣+∣y−1∣≤1|x-1|+|y-1|\le1∣x−1∣+∣y−1∣≤1.Hint 2Start with ∣x∣+∣y∣≤1|x|+|y|\le1∣x∣+∣y∣≤1, then shift it 1 unit upward and 1 unit to the right.Hint 3∣∣x∣−1∣+∣∣y∣−1∣≤1\left||x|-1\right|+\left||y|-1\right|\le1∣∣x∣−1∣+∣∣y∣−1∣≤1Hint 44(2⋅22)=84\left(\frac{2\cdot2}{2}\right)=84(22⋅2)=8Final Answer(B) 888Related Problems (1)AMC 10B/12B 2024 (Problem 14/9)
