At what point the origin be shifted, if the coordinates of a point (-1, 8) become (-7, 3) ?

Answer

To find the point at which the origin should be shifted so that the coordinates of the point (-1, 8) become (-7, 3), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original and New Coordinates:**
- Original coordinates: \( (x, y) = (-1, 8) \)
- New coordinates after shifting the origin: \( (X, Y) = (-7, 3) \)

2. **Set Up the Relationship Between Coordinates:**
- When the origin is shifted to a new point \( (h, k) \), the relationship between the original coordinates and the new coordinates can be expressed as:
\[ x = X + h \quad \text{and} \quad y = Y + k \]

3. **Substitute the Known Values:**
- Substitute the original coordinates and the new coordinates into the equations:
\[ -1 = -7 + h \quad \text{(1)} \]
\[ 8 = 3 + k \quad \text{(2)} \]

4. **Solve for \( h \) from Equation (1):**
- Rearranging equation (1):
\[ h = -1 + 7 = 6 \]

5. **Solve for \( k \) from Equation (2):**
- Rearranging equation (2):
\[ k = 8 - 3 = 5 \]

6. **Conclusion:**
- The origin should be shifted to the point \( (h, k) = (6, 5) \).

### Final Answer:
The origin should be shifted to the point \( (6, 5) \).