rotate (2, 1), (4, 2), and (3, 5) 270 degrees around the origin
To rotate a point (x, y) 270 degrees counterclockwise around the origin, we need to apply the following formula:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Let's calculate the new coordinates for each point:
For (2, 1):
x' = 2 * cos(270°) - 1 * sin(270°)
y' = 2 * sin(270°) + 1 * cos(270°)
Using the values of cos(270°) = 0 and sin(270°) = -1, we get:
x' = 2 * 0 - 1 * (-1) = 1
y' = 2 * (-1) + 1 * 0 = -2
So after rotating (2, 1) 270 degrees counterclockwise around the origin, we get (1, -2).
For (4, 2):
x' = 4 * cos(270°) - 2 * sin(270°)
y' = 4 * sin(270°) + 2 * cos(270°)
Using the values of cos(270°) = 0 and sin(270°) = -1, we get:
x' = 4 * 0 - 2 * (-1) = 2
y' = 4 * (-1) + 2 * 0 = -4
So after rotating (4, 2) 270 degrees counterclockwise around the origin, we get (2, -4).
For (3, 5):
x' = 3 * cos(270°) - 5 * sin(270°)
y' = 3 * sin(270°) + 5 * cos(270°)
Using the values of cos(270°) = 0 and sin(270°) = -1, we get:
x' = 3 * 0 - 5 * (-1) = 5
y' = 3 * (-1) + 5 * 0 = -3
So after rotating (3, 5) 270 degrees counterclockwise around the origin, we get (5, -3).
Therefore, the new coordinates after rotating (2, 1), (4, 2), and (3, 5) 270 degrees counterclockwise around the origin are (1, -2), (2, -4), and (5, -3) respectively.