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).
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).