What is the new point when you rotate a geometric figure with 58 270° counterclockwise about the origin
To rotate a geometric figure counterclockwise about the origin, you need to use the formula:
(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)
where (x, y) are the original coordinates of a point in the figure and θ is the angle of rotation.
In this case, the angle of rotation is 270°. Let's assume the original point is (x, y). Plugging the values into the formula, we get:
(x', y') = (xcos270° - ysin270°, xsin270° + ycos270°)
Simplifying this expression by using the trigonometric values of 270°, we have:
(x', y') = (-ysin270°, xcos270°)
Since sin(270°) = -1 and cos(270°) = 0, the expression becomes:
(x', y') = (-y, 0)
Therefore, when you rotate a geometric figure counterclockwise by 270° about the origin, every point moves to its corresponding new position with the x-coordinate remaining unchanged and the y-coordinate changes sign.