(9,-3) the new point counterclockwise with the origin of 180 degrees?
To find the new point obtained by rotating the point (9, -3) counterclockwise with respect to the origin by 180 degrees, we use the rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
where theta is the angle of rotation.
In this case, theta is 180 degrees. Let's compute the new coordinates:
x' = 9 * cos(180) - (-3) * sin(180)
= 9 * (-1) - (-3) * 0
= -9 - 0
= -9
y' = 9 * sin(180) + (-3) * cos(180)
= 9 * 0 + (-3) * (-1)
= 0 + 3
= 3
Therefore, the new point obtained by rotating (9, -3) counterclockwise with respect to the origin by 180 degrees is (-9, 3).