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?
To rotate a point about the origin 90 degrees clockwise, we can use the following formula:
(x', y') = (x * cos(θ) + y * sin(θ), -x * sin(θ) + y * cos(θ))
In this case, since we want to rotate the point (1, 2) 90 degrees clockwise:
x = 1, y = 2, and θ = 90 degrees.
Plugging these values into the formula, we get:
(x', y') = (1 * cos(90) + 2 * sin(90), -1 * sin(90) + 2 * cos(90))
Calculating the trigonometric functions for 90 degrees:
cos(90) = 0
sin(90) = 1
Substituting these values, we have:
(x', y') = (1 * 0 + 2 * 1, -1 * 1 + 2 * 0)
= (0 + 2, -1 + 0)
= (2, -1)
Therefore, the new point after rotating (1, 2) 90 degrees clockwise about the origin is (2, -1).