Given a point on a geometric figure (1, 2) what is the new point when the point is rotate clockwise about the origin 90 degrees?
To rotate a point clockwise about the origin, we can use the following rotation formula:
x' = x * cos(theta) + y * sin(theta)
y' = -x * sin(theta) + y * cos(theta)
In this case, the point we want to rotate is (1, 2) and we want to rotate it 90 degrees clockwise.
Using the rotation formulas, we have:
x' = 1 * cos(90°) + 2 * sin(90°) = 1 * 0 + 2 * 1 = 2
y' = -1 * sin(90°) + 2 * cos(90°) = -1 * 1 + 2 * 0 = -1
So, the new point after rotating (1, 2) clockwise 90 degrees about the origin is (2, -1).
To find the new point when rotating a point clockwise about the origin by 90 degrees, we can use the following formula:
(x', y') = (x * cos(theta) - y * sin(theta), x * sin(theta) + y * cos(theta))
In this case, the point is (1, 2) and we want to rotate it by 90 degrees. We can substitute the values into the formula:
(x', y') = (1 * cos(90) - 2 * sin(90), 1 * sin(90) + 2 * cos(90))
To simplify the equation, we can use trigonometric identities:
(cos(90) = 0 and sin(90) = 1)
(x', y') = (1 * 0 - 2 * 1, 1 * 1 + 2 * 0)
Simplifying further:
(x', y') = (0 - 2, 1 + 0)
Therefore, the new point after rotating (1, 2) clockwise about the origin by 90 degrees is (-2, 1).