given a point on a line segment (-4,5), what is the new point when the point is rotated counterclockwise about the origin 270 degrees?
To rotate a point counterclockwise about the origin, we can use the following rotation formula:
x' = x*cos(angle) - y*sin(angle)
y' = x*sin(angle) + y*cos(angle)
Here, (x, y) are the coordinates of the original point (-4, 5), and angle is the amount of rotation counterclockwise, which in this case is 270 degrees.
Let's plug in the values:
x' = (-4)*cos(270°) - 5*sin(270°)
y' = (-4)*sin(270°) + 5*cos(270°)
Now, let's calculate:
x' = (-4)*0 - 5*(-1) = 5
y' = (-4)*(-1) + 5*0 = 4
Therefore, the coordinates of the new point after rotating counterclockwise about the origin 270 degrees will be (5, 4).