Given a point on a geometric figure (x, y) what is a new appointment to figure is rotated clockwise about the origin 270 degrees?
To rotate a point (x, y) about the origin clockwise by 270 degrees, you can follow these steps:
Step 1: Convert the point (x, y) to polar coordinates.
- Calculate the distance from the origin to the point using the formula: r = sqrt(x^2 + y^2)
- Calculate the angle the point makes with the positive x-axis using the formula: theta = atan2(y, x)
Step 2: Add 270 degrees to the angle theta to find the new angle.
- Add 270 to theta: new_theta = theta + 270
Step 3: Convert the new polar coordinates (r, new_theta) back to Cartesian coordinates.
- Calculate the new x-coordinate using the formula: new_x = r * cos(new_theta)
- Calculate the new y-coordinate using the formula: new_y = r * sin(new_theta)
So, the new coordinates of the point (x, y) after rotating clockwise by 270 degrees about the origin would be (new_x, new_y).
To rotate a point (x, y) clockwise about the origin by 270 degrees, we can use the following formulas:
New_x = y
New_y = -x
So, if your original point is (x, y), the new rotated point would be:
New_point = (y, -x)