Given a point on a geometric figurè (x, y), what is the new point when the figure is rotated
clockwise about the origin 270 degrees? (1 point)
To find the new point when a figure is rotated clockwise about the origin, we can use the rotation matrix.
The rotation matrix for rotating a point (x, y) clockwise about the origin by an angle θ is given by:
[ cos(θ) sin(θ) ]
[ -sin(θ) cos(θ) ]
In this case, the angle of rotation is 270 degrees, which is equal to 3/2π radians.
Thus, the rotation matrix for rotating a point (x, y) clockwise by 270 degrees is:
[ cos(3/2π) sin(3/2π) ]
[ -sin(3/2π) cos(3/2π) ]
Simplifying this, we get:
[ 0 1 ]
[ -1 0 ]
To find the new coordinates, we multiply the original coordinates (x, y) by the rotation matrix:
[ 0 1 ] [ x ] [ 0*x + 1*y ] [ y ]
[ -1 0 ] * [ y ] = [ -1*x + 0*y ] = [ -x ]
Therefore, the new point when the figure is rotated clockwise about the origin 270 degrees is (-y, x).