The origin is shifted to (2,3) by the translation of axes. If a point P has changed to (0,0), find the coordinates of P in the original system.

Answer

To solve the problem of finding the coordinates of point P in the original coordinate system after the origin has been shifted to (2, 3), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the New Origin and Point P**:
- The new origin after translation is given as \( (H, K) = (2, 3) \).
- The coordinates of point P in the new system are \( (X, Y) = (0, 0) \).

2. **Use the Translation of Axes Formula**:
- The relationship between the old coordinates \( (x, y) \) and the new coordinates \( (X, Y) \) is given by:
\[ X = x - H \]
\[ Y = y - K \]

3. **Substitute the Known Values**:
- From the new coordinates \( (X, Y) = (0, 0) \), we can substitute into the equations:
- For \( X \):
\[ 0 = x - 2 \]
- For \( Y \):
\[ 0 = y - 3 \]

4. **Solve for the Original Coordinates**:
- From the first equation:
\[ x = 2 \]
- From the second equation:
\[ y = 3 \]

5. **Conclusion**:
- The coordinates of point P in the original coordinate system are \( (x, y) = (2, 3) \).

### Final Answer:
The coordinates of point P in the original system are \( (2, 3) \).

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