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Given point A (2, 4)

on the triangle Quadrant I, where is the new point if the triangle is rotated 270 degrees counterclockwise

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To rotate a point \( (x, y) \) around the origin \( (0, 0) \) by 270 degrees counterclockwise, we can use the following transformation:

\[ (x', y') = (y, -x) \]

In your case, the point \( A(2, 4) \) will be transformed as follows:

  1. Identify \( x \) and \( y \):

    • \( x = 2 \)
    • \( y = 4 \)

  2. Apply the transformation:

    • \( x' = y = 4 \)
    • \( y' = -x = -2 \)

Thus, the new point \( A' \) after a 270-degree counterclockwise rotation is:

\[ A'(4, -2) \]

The new point \( (4, -2) \) lies in Quadrant IV.