To determine the new coordinates of the point (17, 14) after a rotation of 270 degrees counterclockwise about the origin, we can use the standard rotation formulas. When a point (x, y) is rotated by an angle θ, the new coordinates (x’, y’) can be calculated by:
x’ = x * cos(θ) – y * sin(θ)
y’ = x * sin(θ) + y * cos(θ)
In our case, θ = 270 degrees. We first convert this angle from degrees to radians since trigonometric functions in most programming environments use radians:
270 degrees = 270 * (π / 180) = 3π/2 radians
Next, we calculate the cosine and sine of 270 degrees:
– cos(270°) = 0
– sin(270°) = -1
Now, substituting x = 17 and y = 14 into our formulas, we get:
x’ = 17 * 0 – 14 * (-1) = 0 + 14 = 14
y’ = 17 * (-1) + 14 * 0 = -17 + 0 = -17
Therefore, the image of the point (17, 14) after a 270-degree counterclockwise rotation about the origin is (14, -17).
Final Result: (14, -17)