Rotating the point C (4,-2) around the origin counterclockwise 270 degrees will put C' at what coordinate
To rotate a point counterclockwise around the origin, you can use the following steps:
1. Identify the coordinates of the point you want to rotate. In this case, the point you want to rotate is C, which has coordinates (4, -2).
2. Determine the angle of rotation. In this case, you want to rotate the point 270 degrees counterclockwise.
3. Apply the rotation formula. The formula to rotate a point (x, y) counterclockwise by an angle θ around the origin is:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Where x' and y' are the coordinates of the new point. In this case, θ = 270 degrees.
4. Substitute the values into the rotation formula:
x' = 4 * cos(270) - (-2) * sin(270)
y' = 4 * sin(270) + (-2) * cos(270)
5. Calculate the values using a calculator:
x' = 4 * 0 - (-2) * (-1) = 0 - 2 = -2
y' = 4 * (-1) + (-2) * 0 = -4 + 0 = -4
Therefore, rotating the point C(4, -2) counterclockwise 270 degrees around the origin will put C' at the coordinate (-2, -4).