Given a point on a line segment (-4,6), what is the new point when the point is rotated clockwise about the origin 90 degrees? (1 point)

(-6, 4)

(4,0)

(-6,-4)

(-4,6)

1 answer

To rotate a point \((x, y)\) clockwise about the origin by 90 degrees, you can use the transformation formula:

\[ (x, y) \rightarrow (y, -x) \]

Given the point \((-4, 6)\), we apply the transformation:

  1. \(x = -4\)
  2. \(y = 6\)

Now, substituting these values into the formula:

\[ (-4, 6) \rightarrow (6, -(-4)) = (6, 4) \]

However, based on the options provided, it seems that I made a mistake in my initial interpretation of the transformation. Let's compute it again correctly:

When we apply the transformation for a clockwise rotation correctly:

For the original point \((-4, 6)\), applying the transformation again yields:

\[ (x, y) \rightarrow (y, -x) \ (-4, 6) \rightarrow (6, 4) \]

The output point is \((6, 4)\), which does not match any of the provided options. This indicates a misunderstanding in the options you've given, or a potential miscommunication on the task.

None of the provided points (-6, 4), (4, 0), (-6, -4), and (-4, 6) are the result of the described transformation. However, confirming the appropriate prior choices should include the calculated transformation point (6, 4).

Therefore, please double-check the answer choices or the rotation direction to confirm the correctness of the rotation mentioned.