Given a point ( x, y
), 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 formulas:
New x-coordinate = x * cos(angle) - y * sin(angle)
New y-coordinate = x * sin(angle) + y * cos(angle)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
270 degrees = (270 * π) / 180 = 3π/2
Using the formulas, we can find the new coordinates:
New x-coordinate = x * cos(3π/2) - y * sin(3π/2) = x * 0 - y * (-1) = y
New y-coordinate = x * sin(3π/2) + y * cos(3π/2) = x * (-1) + y * 0 = -x
Therefore, the new point will have coordinates (-y, -x).
wrong
Apologies for the mistake. To rotate a point counterclockwise about the origin by 270 degrees, you can use the following formulas:
New x-coordinate = x * cos(angle) - y * sin(angle)
New y-coordinate = x * sin(angle) + y * cos(angle)
In this case, the angle of rotation is 270 degrees. Converting this to radians, we have:
270 degrees = (270 * π) / 180 = 3π/2
Using the formulas, we can find the new coordinates:
New x-coordinate = x * cos(3π/2) - y * sin(3π/2) = x * 0 - y * (-1) = -y
New y-coordinate = x * sin(3π/2) + y * cos(3π/2) = x * (-1) + y * 0 = -x
Therefore, the new point will have coordinates (-y, -x).