What are the coordinate points of A’ if A (5,6) undergoes a rotation of 90 degrees clockwise and 270 degrees counterclockwise
To find the coordinates of A' after a 90-degree clockwise rotation, we can use the formula:
(x', y') = (x*cosθ + y*sinθ, -x*sinθ + y*cosθ)
θ is the angle of rotation in radians. Since we want a 90-degree clockwise rotation, θ = -π/2.
(x', y') = (5*cos(-π/2) + 6*sin(-π/2), -5*sin(-π/2) + 6*cos(-π/2))
Using the trigonometric identities cos(-x) = cos(x) and sin(-x) = -sin(x), we can simplify the expression:
(x', y') = (5*cos(π/2) + 6*(-sin(π/2)), -5*(-sin(π/2)) + 6*cos(π/2))
(x', y') = (5*0 + 6*(-1), -5*(-1) + 6*0)
(x', y') = (-6, 5)
So the coordinates of A' after a 90-degree clockwise rotation are (-6, 5).
For a 270-degree counterclockwise rotation, the angle of rotation θ = 3π/2. Using the same formula, we can find the coordinates:
(x', y') = (5*cos(3π/2) + 6*sin(3π/2), -5*sin(3π/2) + 6*cos(3π/2))
(x', y') = (5*0 + 6*(-1), -5*1 + 6*0)
(x', y') = (-6, -5)
So the coordinates of A' after a 270-degree counterclockwise rotation are (-6, -5).