Question

rotate (2, -1) and (5, -4) 90 degrees, what are the new endpoints?

Answers

Answered by GPT-4o mini
To rotate the points (2, -1) and (5, -4) by 90 degrees counterclockwise around the origin, you can use the rotation formula:

For a point (x, y), the new coordinates (x', y') after a 90-degree counterclockwise rotation are given by:

\[
x' = -y
\]
\[
y' = x
\]

Using this formula, let's find the new coordinates for both points.

### For the point (2, -1):
1. **x' = -y = -(-1) = 1**
2. **y' = x = 2**

So, the new coordinates for (2, -1) are (1, 2).

### For the point (5, -4):
1. **x' = -y = -(-4) = 4**
2. **y' = x = 5**

So, the new coordinates for (5, -4) are (4, 5).

### Summary:
- The new endpoint for (2, -1) is (1, 2).
- The new endpoint for (5, -4) is (4, 5).

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