Given a point ( x, y ) what is the new point when the point is rotate counterclockwise about the origin 270 degrees?
To rotate a point counterclockwise about the origin, you can use the following formulas:
New_x = x * cos(angle) - y * sin(angle)
New_y = x * sin(angle) + y * cos(angle)
In this case, since we want to rotate the point 270 degrees counterclockwise about the origin, we substitute angle = 270 degrees.
Using these formulas, we can calculate the new coordinates:
New_x = x * cos(270) - y * sin(270)
New_y = x * sin(270) + y * cos(270)
However, it's important to note that sin(270) = -1 and cos(270) = 0.
So the formulas simplify to:
New_x = x * 0 - y * (-1)
= y
New_y = x * (-1) + y * 0
= -x
Therefore, the new point (x', y') after rotating the original point (x, y) counterclockwise about the origin 270 degrees is:
x' = y
y' = -x
y, -x is the answer. ^^
When a point (x, y) is rotated counterclockwise about the origin by 270 degrees, the new point can be obtained by swapping the x and y-coordinates and changing the sign of the new x-coordinate.
So, the new point is (-y, x).