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 formulas:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Where (x, y) are the original coordinates of the point, (x', y') are the coordinates of the new point after rotation, and theta is the rotation angle.
In this case, the original coordinates of the point are (-4, 5), and we want to rotate it counterclockwise by 270 degrees.
Let's substitute the values into the formulas:
x' = (-4) * cos(270) - 5 * sin(270)
y' = (-4) * sin(270) + 5 * cos(270)
Since cos(270) = 0 and sin(270) = -1, we can simplify:
x' = (-4) * 0 - 5 * (-1)
y' = (-4) * (-1) + 5 * 0
x' = 0 + 5 = 5
y' = 4 + 0 = 4
Therefore, the new coordinates of the point after rotating counterclockwise about the origin by 270 degrees are (5, 4).
To rotate a point counterclockwise about the origin, we can use the following formulas:
For a point (x, y) rotated counterclockwise by θ degrees:
x' = x*cos(θ) - y*sin(θ)
y' = x*sin(θ) + y*cos(θ)
In this case, we want to rotate the point (-4, 5) counterclockwise by 270 degrees.
Using the formulas mentioned above, we have:
x' = -4*cos(270) - 5*sin(270)
y' = -4*sin(270) + 5*cos(270)
Now, we substitute the values of cos(270) and sin(270) to simplify the equations:
x' = -4*0 - 5*(-1) = 5
y' = -4*1 + 5*0 = -4
Therefore, the new point after rotating (-4, 5) counterclockwise 270 degrees about the origin is (5, -4).