Given a point on a line segment (−4, 5) , what is the new point when the point is rotated counterclockwise about the origin 270 degrees?(1 point)
To rotate a point counterclockwise about the origin, we can use the following rotation matrix:
[cos(theta) -sin(theta)]
[sin(theta) cos(theta)]
In this case, since we want to rotate 270 degrees counterclockwise, we use theta = 270 degrees or theta = -90 degrees (since 270 degrees is the same as rotating -90 degrees).
Using the rotation matrix, we can calculate the new coordinates as follows:
[x'] = [cos(-90) -sin(-90)] * [x]
[y'] = [sin(-90) cos(-90)] * [y]
where (x, y) are the original coordinates and (x', y') are the new coordinates.
Plugging in the values, we get:
[x'] = [cos(-90) -sin(-90)] * [-4] = [0 -(-4)] = [0 4]
[y'] = [sin(-90) cos(-90)] * [5] = [-1 0] * [5] = [-5 0]
Therefore, the new point after rotating 270 degrees counterclockwise about the origin is (0, 4).