Give a point (x,y), what is the new point when the point is rotated counterclockwise about the origin 270 degrees?

Answer 1

To rotate a point counterclockwise about the origin, we can use the following formulas:

x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)

Given that we are rotating the point 270 degrees counterclockwise, we need to substitute theta with π/2 in the formulas.

x' = x*cos(π/2) - y*sin(π/2) = 0 - y*(-1) = y
y' = x*sin(π/2) + y*cos(π/2) = x*1 + 0 = x

Therefore, the new point is (y, x).