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Given point A (2, 4) on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise? (1 point)

(−4, 2) left parenthesis negative 4 comma 2 right parenthesis (−2,−4) left parenthesis negative 2 comma negative 4 right parenthesis (4,−2) left parenthesis 4 comma negative 2 right parenthesis (−4,−2)

1 answer

To find the new point after rotating point A (2, 4) by 90 degrees counterclockwise, we can use the following transformation formula:

If a point (x, y) is rotated 90 degrees counterclockwise around the origin, the new coordinates (x', y') are given by: \[ x' = -y \] \[ y' = x \]

Applying this transformation to point A (2, 4):

  1. Calculate the new x-coordinate: \[ x' = -y = -4 \]

  2. Calculate the new y-coordinate: \[ y' = x = 2 \]

Thus, the rotated point is (-4, 2).

Therefore, the new point after rotating point A (2, 4) 90 degrees counterclockwise is \((-4, 2)\).