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Omni-MATH / Consider the following transformation of the Cartesian plane: choose a lattice…

Problem

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problem

Consider the following transformation of the Cartesian plane: choose a lattice point and rotate the plane 90∘90^\circ counterclockwise about that lattice point. Is it possible, through a sequence of such transformations, to take the triangle with vertices (0,0)(0,0), (1,0)(1,0) and (0,1)(0,1) to the triangle with vertices (0,0)(0,0), (1,0)(1,0) and (1,1)(1,1)?
Plain-text mathematical notation (without MathML)
Consider the following transformation of the Cartesian plane: choose a lattice point and rotate the plane 90^(∘) counterclockwise about that lattice point. Is it possible, through a sequence of such transformations, to take the triangle with vertices (0,0), (1,0) and (0,1) to the triangle with vertices (0,0), (1,0) and (1,1)?
Original LaTeX notation
Consider the following transformation of the Cartesian plane: choose a lattice point and rotate the plane $90^\circ$ counterclockwise about that lattice point. Is it possible, through a sequence of such transformations, to take the triangle with vertices $(0,0)$, $(1,0)$ and $(0,1)$ to the triangle with vertices $(0,0)$, $(1,0)$ and $(1,1)$?

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Source and history

task_id
3bdb052d-7880-5b09-abce-821968679870
task_key
test--3bdb052d-7880-5b09-abce-821968679870
task_revision_id
1
config / split
/ test

Official source

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