The point L(–4,–5) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, L'?

1. Break Down the Problem

To rotate a point 90° counterclockwise around the origin, we need to transform the coordinates of the point using a specific transformation rule associated with this rotation.

2. Relevant Concepts

The rotation of a point $(x, y)$ by 90° counterclockwise around the origin can be done using the following transformation: $(x', y') = (-y, x)$ where $(x', y')$ are the new coordinates after the rotation.

3. Analysis and Detail

Given the point $L(-4, -5)$:

• Here, $x = -4$ and $y = -5$.
• Applying the rotation formula: $x' = -y = -(-5) = 5$ $y' = x = -4$ So, the new coordinates after the rotation would be: $L' = (5, -4)$

4. Verify and Summarize

We have rotated the point by applying the transformation correctly, and the calculated new coordinates are consistent with the rotation definition. Thus, the resulting point after rotation is validated.

Final Answer

The coordinates of the resulting point $L'$ after rotation are $(5, -4)$.