Given point A (2, 4) on the triangle in Quadrant I, how would you describe the coordinates of the new point when the triangle is rotated 90 degrees clockwise?
(1 point)
Responses
(−4, 2)
left parenthesis negative 4 comma 2 right parenthesis
(4,−2)
left parenthesis 4 comma negative 2 right parenthesis
(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis
(−2,−4)
None of the given options correctly describe the coordinates of the new point when the triangle is rotated 90 degrees clockwise.
To find the coordinates of the new point, we need to perform the clockwise rotation using the formulas:
x' = x * cos(angle) + y * sin(angle)
y' = -x * sin(angle) + y * cos(angle)
Applying these formulas for a rotation of 90 degrees clockwise (angle = -90 degrees):
x' = 2 * cos(-90) + 4 * sin(-90) = 2 * 0 - 4 * 1 = -4
y' = -2 * sin(-90) + 4 * cos(-90) = -2 * (-1) + 4 * 0 = 2
Therefore, the new point after a 90 degrees clockwise rotation would have coordinates (-4, 2).