Rotate the point (5, 8) on a geometric figure 270 degrees clockwise. What is the new point? (1 point)
To rotate a point 270 degrees clockwise, we can use the formula:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
Where:
x, y: coordinates of the original point
θ: angle of rotation in radians
In this case, the original point is (5, 8), and we want to rotate it 270 degrees clockwise.
Converting 270 degrees to radians:
270 degrees = (270 * π) / 180 = 3π/2 radians
Using the formula:
(x', y') = (5*cos(3π/2) - 8*sin(3π/2), 5*sin(3π/2) + 8*cos(3π/2))
Since cos(3π/2) = 0 and sin(3π/2) = -1, the formula simplifies to:
(x', y') = (-8, 5)
Therefore, the new point after rotating (5, 8) 270 degrees clockwise is (-8, 5).