Question
rotate (8,7) centered around (0, 0)
Answers
GPT 3.5
To rotate the point (8, 7) around the origin (0, 0), we can use the rotation formula.
The rotation formula is given by:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
where (x, y) is the original point, (x', y') is the rotated point, and theta is the angle of rotation.
Since we want to rotate around the origin, the center of rotation is (0, 0). Let's assume the angle of rotation is 45 degrees.
Substituting the values into the rotation formula, we have:
x' = 8 * cos(45) - 7 * sin(45)
y' = 8 * sin(45) + 7 * cos(45)
Evaluating these expressions:
x' = 8 * 0.7071 - 7 * 0.7071 ≈ 5.6569
y' = 8 * 0.7071 + 7 * 0.7071 ≈ 14.1421
Therefore, the point (8, 7) rotated 45 degrees around the origin (0, 0) is approximately (5.6569, 14.1421).
The rotation formula is given by:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
where (x, y) is the original point, (x', y') is the rotated point, and theta is the angle of rotation.
Since we want to rotate around the origin, the center of rotation is (0, 0). Let's assume the angle of rotation is 45 degrees.
Substituting the values into the rotation formula, we have:
x' = 8 * cos(45) - 7 * sin(45)
y' = 8 * sin(45) + 7 * cos(45)
Evaluating these expressions:
x' = 8 * 0.7071 - 7 * 0.7071 ≈ 5.6569
y' = 8 * 0.7071 + 7 * 0.7071 ≈ 14.1421
Therefore, the point (8, 7) rotated 45 degrees around the origin (0, 0) is approximately (5.6569, 14.1421).