When the origin is shifted to (4,-5) by the translation of axes, find the coordinates of the point
(4,-5) with reference to new axes.

Answer

To find the coordinates of the point (4, -5) with reference to the new axes after shifting the origin to (4, -5), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Coordinates**:
The original coordinates of the point are given as (4, -5).

2. **Determine the Shift in Origin**:
The origin is shifted to the point (4, -5). This means that the new origin (h, k) is (4, -5).

3. **Set Up the Transformation Equations**:
When the origin is shifted, the new coordinates (X, Y) can be calculated using the following equations:
\[ X = x - h \]
\[ Y = y - k \]
Here, (x, y) are the original coordinates, and (h, k) are the coordinates of the new origin.

4. **Substitute the Values**:
Substitute the original coordinates (4, -5) and the shift (4, -5) into the equations:
- For X:
\[ X = 4 - 4 = 0 \]
- For Y:
\[ Y = -5 - (-5) = -5 + 5 = 0 \]

5. **Conclusion**:
Therefore, the coordinates of the point (4, -5) with reference to the new axes are (0, 0).

### Final Answer:
The coordinates of the point (4, -5) with respect to the new axes are (0, 0).

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