Solution to Exercise 3.60.
Geometry existed before the creation.
—
Plato (427–347? BCE)
Exercise 3.60. Find a direct isometry that maps X(1, 1, 1)
to X'(1, 1, 1) and Y(3, 0, 1) to Y'(0, 3, 1). Is it a
translation or a rotation?
implies
implies
Solve the system of four equations in four unknowns
to obtain
.
Hence, a direct isometry is which is a rotation about the origin by
