Given a point on a geometric figure (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 the figure is rotated clockwise about the origin 270 degrees, we can apply the rotation matrix:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]
In this case, since we are rotating 270 degrees clockwise, the angle of rotation (θ) is -270 degrees.
Using the rotation matrix:
[ cos(-270) -sin(-270) ]
[ sin(-270) cos(-270) ]
Simplifying the trigonometric functions:
[ cos(90) sin(90) ]
[ -sin(90) cos(90) ]
Evaluating the trigonometric functions:
[ 0 1 ]
[ -1 0 ]
Now, multiplying the rotation matrix with the original point (x, y) using matrix multiplication:
[ 0 1 ] [ x ] [ 0*x + 1*y ] [ y ]
[ -1 0 ] * [ y ] = [ -1*x + 0*y ] = [ -x ]
Therefore, the new point after rotating the figure 270 degrees clockwise about the origin is (-y, x).