Give a point (x,y), what is the new point when the point is rotated counterclockwise about the origin 270°?
When a point is rotated counterclockwise about the origin, the x-coordinate and y-coordinate of the point change according to the rotation formula:
New x-coordinate = x * cos(angle) - y * sin(angle)
New y-coordinate = x * sin(angle) + y * cos(angle)
In this case, since we want to rotate the point 270° counterclockwise, we can substitute angle = 270° into the rotation formula:
New x-coordinate = x * cos(270°) - y * sin(270°)
New y-coordinate = x * sin(270°) + y * cos(270°)
Since cos(270°) = 0 and sin(270°) = -1, the formulas simplify to:
New x-coordinate = -y
New y-coordinate = x
Therefore, the new point after rotating the given point counterclockwise about the origin 270° is (-y, x).