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Omni-MATH / Plot points A,B,C at coordinates (0,0),(0,1), and (1,1) in the plane, respectively. Let S denote the union of the two line segments AB and BC. Let X₁ be the area swept out when Bob…

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problem

Plot points A,B,CA, B, C at coordinates (0,0),(0,1)(0,0),(0,1), and (1,1)(1,1) in the plane, respectively. Let SS denote the union of the two line segments ABA B and BCB C. Let X1X_{1} be the area swept out when Bobby rotates SS counterclockwise 45 degrees about point AA. Let X2X_{2} be the area swept out when Calvin rotates SS clockwise 45 degrees about point AA. Find X1+X22\frac{X_{1}+X_{2}}{2}.
Plain-text mathematical notation (without MathML)
Plot points A,B,C at coordinates (0,0),(0,1), and (1,1) in the plane, respectively. Let S denote the union of the two line segments AB and BC. Let X₁ be the area swept out when Bobby rotates S counterclockwise 45 degrees about point A. Let X₂ be the area swept out when Calvin rotates S clockwise 45 degrees about point A. Find (X₁+X₂)/(2).
Original LaTeX notation
Plot points $A, B, C$ at coordinates $(0,0),(0,1)$, and $(1,1)$ in the plane, respectively. Let $S$ denote the union of the two line segments $A B$ and $B C$. Let $X_{1}$ be the area swept out when Bobby rotates $S$ counterclockwise 45 degrees about point $A$. Let $X_{2}$ be the area swept out when Calvin rotates $S$ clockwise 45 degrees about point $A$. Find $\frac{X_{1}+X_{2}}{2}$.

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Source and history

task_id
92b9086e-e6fc-5152-8ff4-55429ad31738
task_key
test--92b9086e-e6fc-5152-8ff4-55429ad31738
task_revision_id
1
config / split
/ test

Official source

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