Given point A (2, 4) on the triangle in Quadrant 1, where is the new point if the triangle is rotated 270° counterclockwise
To rotate a point counterclockwise on the coordinate plane, we can use the following formulas:
x' = x * cos(θ) - y * sin(θ)
y' = x * sin(θ) + y * cos(θ)
Since we want to rotate the point A (2, 4) counterclockwise by 270°, we substitute θ = 270° into the formulas:
x' = 2 * cos(270°) - 4 * sin(270°)
y' = 2 * sin(270°) + 4 * cos(270°)
To simplify these expressions, we can use the trigonometric identities:
cos(270°) = 0
sin(270°) = -1
x' = 2 * (0) - 4 * (-1) = 4
y' = 2 * (-1) + 4 * (0) = -2
Therefore, the new point after rotating A (2, 4) counterclockwise by 270° is B(4, -2).