Given a point on a geometric figure (1, 2), what is the new point when the point is rotated clockwise about the origin 90 degrees?(1 point)
To rotate a point clockwise about the origin 90 degrees, you can use the following formulas:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
In this case, the point is (1, 2), and we want to rotate it 90 degrees clockwise. The angle of rotation (θ) will be -90 degrees (-π/2 radians), since it's clockwise.
Let's calculate the new coordinates:
x' = 1 * cos(-90°) - 2 * sin(-90°)
= 1 * cos(-π/2) - 2 * sin(-π/2)
= 1 * 0 - 2 * (-1)
= 2
y' = 1 * sin(-90°) + 2 * cos(-90°)
= 1 * sin(-π/2) + 2 * cos(-π/2)
= 1 * (-1) + 2 * 0
= -1
Therefore, the new point when the point (1, 2) is rotated clockwise 90 degrees about the origin is (2, -1).