Question

Given a point (1, 2) on a geometric figure what is the new point when the rotated counterclockwise about the origin 90 degrees?

Answer 1

To rotate a point counterclockwise about the origin, we can use the following formula:

New point (x', y') = (x * cosθ - y * sinθ, x * sinθ + y * cosθ)

Given the point (1, 2) and rotating it counterclockwise by 90 degrees:

θ = 90° = π/2 rad

Substituting the values into the formula:

x' = 1 * cos(π/2) - 2 * sin(π/2) = 1 * 0 - 2 * 1 = -2
y' = 1 * sin(π/2) + 2 * cos(π/2) = 1 * 1 + 2 * 0 = 1

Therefore, the new point when the given point (1, 2) is rotated counterclockwise about the origin by 90 degrees is (-2, 1).