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, you can use the formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, the point is (-4, 5) and the rotation angle is 270 degrees counterclockwise.
Converting 270 degrees to radians:
270 degrees = (270 * π) / 180 = 3π / 2 radians.
Using the formula, we can substitute the values:
x' = (-4) * cos(3π / 2) - 5 * sin(3π / 2)
y' = (-4) * sin(3π / 2) + 5 * cos(3π / 2)
Calculating cosine and sine of 3π / 2:
cos(3π / 2) = 0
sin(3π / 2) = -1
Substituting the values:
x' = (-4) * 0 - 5 * (-1) = 0 + 5 = 5
y' = (-4) * (-1) + 5 * 0 = 4 + 0 = 4
Therefore, the new point after rotating (-4, 5) counterclockwise about the origin by 270 degrees is (5, 4).
To rotate a point counterclockwise about the origin, you can use the following formula:
X' = X * cos(theta) - Y * sin(theta)
Y' = X * sin(theta) + Y * cos(theta)
In this case, the given point is (4, 5) and it needs to be rotated counterclockwise by 270 degrees.
Let's substitute the values into the formula:
X' = 4 * cos(270°) - 5 * sin(270°)
Y' = 4 * sin(270°) + 5 * cos(270°)
To simplify the calculations, we can use the fact that cos(270°) = 0 and sin(270°) = -1.
X' = 4 * 0 - 5 * (-1) = 0 + 5 = 5
Y' = 4 * (-1) + 5 * 0 = -4 + 0 = -4
Therefore, the new point after rotating (4, 5) counterclockwise about the origin by 270 degrees is (5, -4).