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AMC 12 Mock Exam 4 Problem 7

Problem 7 of 25

The lines y=2xy=2x and y=−12x+10y=-\tfrac12x+10 and the xx-axis bound a triangle. What is the area of that triangle?

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Solution

The lines meet where 2x=−12x+102x=-\frac12x+10, i.e., at (4,8)(4,8). The line y=2xy=2x meets the xx-axis at (0,0)(0,0), and y=−12x+10y=-\frac12x+10 meets it at (20,0)(20,0). The triangle has base 2020 and height 88, so its area is 12⋅20⋅8=80\frac12\cdot20\cdot8=\boxed{80}.

Tagged: coordinate geometry: area bounded by lines