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Rotate the point (−4, −6) on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point) Responses (−6, −4) left parenthesis negative 6 comma negative 4 right parenthesis (−6, 4) left parenthesis negative 6 comma 4 right parenthesis (6, −4) left parenthesis 6 comma negative 4 right parenthesis (6, 4) left parenthesis 6 comma 4 right parenthesis

1 answer

To rotate the point \((-4, -6)\) 90 degrees counterclockwise, you can use the formula for rotation of points in the Cartesian plane.

The general rule for rotating a point \((x, y)\) 90 degrees counterclockwise around the origin is:

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

Applying this to the point \((-4, -6)\):

  1. Identify \(x = -4\) and \(y = -6\).
  2. Replace using the rule:
    • New \(x = -(-6) = 6\)
    • New \(y = -4\)

Thus, the new point is \((6, -4)\).

Therefore, the correct response is:

\((6, -4)\)