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??
To find the new point when a figure is rotated clockwise about the origin, you can use the rotation matrix.
The rotation matrix for rotating a point (x, y) clockwise about the origin by an angle θ is:
[ cos(θ) -sin(θ) ]
[ sin(θ) cos(θ) ]
In this case, the angle of rotation is 270 degrees, which is equivalent to 3π/2 radians.
So, the rotation matrix for a clockwise rotation of 270 degrees is:
[ cos(3π/2) -sin(3π/2) ]
[ sin(3π/2) cos(3π/2) ]
Calculating the values, we have:
[ 0 -1 ]
[ 1 0 ]
To find the new point, we multiply the rotation matrix by the coordinates of the original point (x, y).
New point = [ 0 -1 ] * [ x ]
[ y ]
This gives us the new coordinates (x', y'):
x' = 0 * x + (-1) * y = -y
y' = 1 * x + 0 * y = x
Therefore, the new point after rotating (x, y) 270 degrees clockwise about the origin is (-y, x).