given A (2, 4) on the triangle in Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise
To find the new position after rotating the point A(2, 4) 270 degrees counterclockwise, we can use the rotation formula.
The rotation formula for counterclockwise rotation about the origin by θ degrees is:
(x', y') = (x*cosθ - y*sinθ, x*sinθ + y*cosθ)
In this case, θ = 270 degrees.
Substituting the values of x = 2, y = 4, and θ = 270 into the formula:
(x', y') = (2*cos(270) - 4*sin(270), 2*sin(270) + 4*cos(270))
Since cos(270) = 0 and sin(270) = -1, we get:
(x', y') = (2*0 - 4*(-1), 2*(-1) + 4*0)
= (0 + 4, -2 + 0)
= (4, -2)
Therefore, the new point after rotating A(2, 4) 270 degrees counterclockwise is B(4, -2).