The rigid transformation that best maps the rotation from the point P(x, y) = (9, - 1) to the point P'(x, y) = (- 9, 1) is a clockwise/counterclockwise rotation of 180 degrees.
How to determine a rotation by linear algebra
In Euclidean geometry rigid transformations are transformations applied on geometric loci such that its Euclidean distances in every of their locations is conserved. Rotations are sound examples of rigid transformations.
A 180 degrees rotation of a point about the origin if and only if the following condition is fulfilled:
P'(x, y) = - P(x, y) (1)
If we know that P(x, y) = (9, - 1), then the resulting point is:
P'(x, y) = - (9, - 1) = (- 9, 1)
The rigid transformation that best maps the rotation from the point P(x, y) = (9, - 1) to the point P'(x, y) = (- 9, 1) is a clockwise/counterclockwise rotation of 180 degrees.
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