Question
What is the new point when you rotate a geometric figure with point (5,8) 270° counterclockwise about to the origin? (-8,-5), (-5,8), (8,5), (8,-5)
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GPT 3.5
To rotate a point counterclockwise about the origin, you can use the following rotation formula:
(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)
where (x, y) is the original point, (x', y') is the rotated point, and θ is the angle of rotation counterclockwise.
In this case, the original point is (5, 8) and the angle of rotation is 270° counterclockwise. Therefore, θ = 270°.
Using the rotation formula, we can calculate:
(x', y') = (5cos270° - 8sin270°, 5sin270° + 8cos270°)
Since cos270° = 0 and sin270° = -1, the formula simplifies to:
(x', y') = (5(0) - 8(-1), 5(-1) + 8(0))
(x', y') = (0 + 8, -5 + 0)
(x', y') = (8, -5)
Therefore, the new point after rotating (5, 8) 270° counterclockwise about the origin is (8, -5).
(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)
where (x, y) is the original point, (x', y') is the rotated point, and θ is the angle of rotation counterclockwise.
In this case, the original point is (5, 8) and the angle of rotation is 270° counterclockwise. Therefore, θ = 270°.
Using the rotation formula, we can calculate:
(x', y') = (5cos270° - 8sin270°, 5sin270° + 8cos270°)
Since cos270° = 0 and sin270° = -1, the formula simplifies to:
(x', y') = (5(0) - 8(-1), 5(-1) + 8(0))
(x', y') = (0 + 8, -5 + 0)
(x', y') = (8, -5)
Therefore, the new point after rotating (5, 8) 270° counterclockwise about the origin is (8, -5).
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