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

Answer

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

### Step 1: Understand the Shift in Origin
The origin has been shifted from (0, 0) to (2, 3). This means that every point in the new coordinate system will have its coordinates adjusted by this shift.

### Step 2: Define the New Coordinates
Let the coordinates of point P in the new system be given as (4, 5). Here, we denote:
- Capital X (X') = 4 (new x-coordinate)
- Capital Y (Y') = 5 (new y-coordinate)

### Step 3: Identify the Shift in Coordinates
The shift in the x and y coordinates due to the origin change is:
- Δx = 2 (shift in x-direction)
- Δy = 3 (shift in y-direction)

### Step 4: Calculate the Original Coordinates
To find the original coordinates (x, y) in the original system, we use the formulas:
- \( x = X' - Δx \)
- \( y = Y' - Δy \)

Substituting the values:
- For x:
\[ x = 4 - 2 = 2 \]
- For y:
\[ y = 5 - 3 = 2 \]

### Step 5: Write the Final Coordinates
Thus, the coordinates of point P in the original system are:
\[ (x, y) = (2, 2) \]

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

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