What are the coordinates of (5,6) if it undergoes a rotation of 270 degrees clockwise

Answer 1

To find the coordinates of a point after a rotation of 270 degrees clockwise, we can use a rotation matrix.

The rotation matrix for a rotation of θ degrees clockwise is:

[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]

In this case, θ = 270 degrees, so the rotation matrix becomes:

[ cos(270) -sin(270) ]
[ sin(270) cos(270) ]

Simplifying:

[ 0 -1 ]
[ 1 0 ]

To apply this rotation matrix to the point (5, 6), we multiply:

[ 0 -1 ] [ 5 ] = [ (-1)(5) + (0)(6) ] = [ -5 ]
[ 1 0 ] [ 6 ] [ (0)(5) + (1)(6) ] [ 6 ]

Therefore, the coordinates of (5, 6) after a rotation of 270 degrees clockwise are (-5, 6).