Which of the following are the correct coordinates when the point (-4,-6) is rotated 90° anticlockwise about the origin?

1. Break Down the Problem

To find the new coordinates after rotating the point $(-4, -6)$ by 90° anticlockwise (counterclockwise) about the origin, we'll use the standard rotation formula.

2. Relevant Concepts

The formula for rotating a point $(x, y)$ by an angle $\theta$ (in degrees) around the origin is given by: $(x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta)$ For a 90° rotation anticlockwise, $\theta = 90^\circ$. Thus, we use: $\cos(90^\circ) = 0 \quad \text{and} \quad \sin(90^\circ) = 1$

3. Analysis and Detail

Substituting the values into the formula:

• Given point: $(x, y) = (-4, -6)$
• Calculate $x'$ and $y'$: $x' = -4 \cdot 0 - (-6) \cdot 1 = 0 + 6 = 6$ $y' = -4 \cdot 1 + (-6) \cdot 0 = -4 + 0 = -4$ Thus, the new coordinates after the rotation are $(6, -4)$.

4. Verify and Summarize

We checked our calculations, and they are correct. The point $(-4, -6)$ rotates to $(6, -4)$ when rotated 90° anticlockwise about the origin.

Final Answer

The correct coordinates after the rotation are $(6, -4)$.