Find the new coordinates of point `(3,4)` if the origin is shifted to (1, 2) by a translation.

Explanation

To find the new coordinates of the point (3, 4) after shifting the origin to (1, 2), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Old and New Origin**:
- The old origin is (0, 0).
- The new origin after translation is (1, 2).

2. **Define the Old Coordinates**:
- The old coordinates of the point are given as (x, y) = (3, 4).

3. **Define the New Coordinates**:
- Let the new coordinates be (x', y').

4. **Establish the Relationship Between Old and New Coordinates**:
- The relationship between the old coordinates and the new coordinates can be expressed as:
- \( x = x' + h \)
- \( y = y' + k \)
- Here, \( h \) is the x-coordinate of the new origin (1) and \( k \) is the y-coordinate of the new origin (2).

5. **Substitute Known Values**:
- For the x-coordinate:
- \( 3 = x' + 1 \)
- For the y-coordinate:
- \( 4 = y' + 2 \)

6. **Solve for x'**:
- Rearranging the equation for x:
- \( x' = 3 - 1 = 2 \)

7. **Solve for y'**:
- Rearranging the equation for y:
- \( y' = 4 - 2 = 2 \)

8. **State the New Coordinates**:
- The new coordinates after the translation are (x', y') = (2, 2).

### Final Answer:
The new coordinates of the point (3, 4) after shifting the origin to (1, 2) are (2, 2).

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