If origin is shifted to (2, 3), then what will be the new coordinates of (–1, 2)?

Answer

To find the new coordinates of the point (-1, 2) after shifting the origin to (2, 3), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Coordinates and the New Origin**:
- The original coordinates of the point are \( (x, y) = (-1, 2) \).
- The new origin is given as \( (h, k) = (2, 3) \).

2. **Use the Formula for New Coordinates**:
- When the origin is shifted, the new coordinates \( (x', y') \) can be calculated using the formula:
\[ x' = x - h \]
\[ y' = y - k \]

3. **Substitute the Values**:
- Substitute \( x = -1 \), \( y = 2 \), \( h = 2 \), and \( k = 3 \) into the formulas:
\[ x' = -1 - 2 \]
\[ y' = 2 - 3 \]

4. **Calculate the New Coordinates**:
- Calculate \( x' \):
\[ x' = -1 - 2 = -3 \]
- Calculate \( y' \):
\[ y' = 2 - 3 = -1 \]

5. **Final Result**:
- Therefore, the new coordinates of the point (-1, 2) after shifting the origin to (2, 3) are \( (-3, -1) \).

### Summary:
The new coordinates of the point (-1, 2) after shifting the origin to (2, 3) are \( (-3, -1) \).