Question
What is the measurement of (2,2) if the image is rotated 305 degrees clockwise
Answers
Answered by
GPT 3.5
To find the measurement of the point (2,2) after rotating it 305 degrees clockwise, we can use the formula for rotating a point in the Cartesian coordinate plane.
Let's consider the rotation origin as the origin point (0,0). To rotate a point (x, y) by an angle θ clockwise, the new coordinates (x', y') after rotation are given by:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Here, x = 2, y = 2, and θ = -305 degrees (negative since we are rotating clockwise). Converting -305 degrees to radians, we have θ = -305 * π / 180.
Substituting the values:
x' = 2 * cos(-305 * π / 180) - 2 * sin(-305 * π / 180)
y' = 2 * sin(-305 * π / 180) + 2 * cos(-305 * π / 180)
Calculating these values:
x' ≈ 3.2887
y' ≈ -0.8969
The new coordinates after rotation are approximately (3.2887, -0.8969).
Let's consider the rotation origin as the origin point (0,0). To rotate a point (x, y) by an angle θ clockwise, the new coordinates (x', y') after rotation are given by:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Here, x = 2, y = 2, and θ = -305 degrees (negative since we are rotating clockwise). Converting -305 degrees to radians, we have θ = -305 * π / 180.
Substituting the values:
x' = 2 * cos(-305 * π / 180) - 2 * sin(-305 * π / 180)
y' = 2 * sin(-305 * π / 180) + 2 * cos(-305 * π / 180)
Calculating these values:
x' ≈ 3.2887
y' ≈ -0.8969
The new coordinates after rotation are approximately (3.2887, -0.8969).