Given a point on a geometric figure (x, y)

Question

, what is the new point when the figure is rotated clockwise about the origin 270 degrees?(1 point)

Answer 1

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).