Given point A (2, 4) on the triangle quadrant I where is the new point if the triangle is rotated 270 degrees counterclockwise?
To rotate a point counterclockwise by 270 degrees, we can make use of the following rotation formula:
new_x = old_x * cos(theta) - old_y * sin(theta)
new_y = old_x * sin(theta) + old_y * cos(theta)
In this case, since we are rotating counterclockwise by 270 degrees, theta is equal to 270 degrees in radians. Converting degrees to radians, we get:
theta = 270 * pi / 180 = 3 * pi / 2
Substituting the values into the rotation formula, we have:
new_x = 2 * cos(3 * pi / 2) - 4 * sin(3 * pi / 2)
new_y = 2 * sin(3 * pi / 2) + 4 * cos(3 * pi / 2)
cos(3 * pi / 2) = 0
sin(3 * pi / 2) = -1
new_x = 2 * 0 - 4 * (-1) = 4
new_y = 2 * (-1) + 4 * 0 = -2
Therefore, the new point after rotating the triangle counterclockwise by 270 degrees is (4, -2).