If(-4,3) are the coordinates of a point P in the new system when the origin is shifted to (1,5), then find original coordinatres of P.

Answer

To find the original coordinates of point P given its new coordinates after a shift in the origin, we can follow these steps:

### Step 1: Understand the Shift in Origin
The new coordinates of point P are given as (-4, 3). The origin has been shifted to (1, 5). This means that the new coordinates (X, Y) relate to the original coordinates (x, y) as follows:

\[ X = x + \Delta X \]
\[ Y = y + \Delta Y \]

Where \(\Delta X\) and \(\Delta Y\) are the shifts in the x and y directions, respectively.

### Step 2: Identify the Shift Values
From the problem, we can identify:
- \(\Delta X = 1\) (the x-coordinate of the new origin)
- \(\Delta Y = 5\) (the y-coordinate of the new origin)

### Step 3: Set Up the Equations
Using the formulas from Step 1, we can set up the equations:
1. For the x-coordinate:
\[ -4 = x + 1 \]
2. For the y-coordinate:
\[ 3 = y + 5 \]

### Step 4: Solve for x
From the first equation:
\[ -4 = x + 1 \]
Subtract 1 from both sides:
\[ x = -4 - 1 \]
\[ x = -5 \]

### Step 5: Solve for y
From the second equation:
\[ 3 = y + 5 \]
Subtract 5 from both sides:
\[ y = 3 - 5 \]
\[ y = -2 \]

### Step 6: Write the Original Coordinates
Now that we have both x and y, we can write the original coordinates of point P:
\[ (x, y) = (-5, -2) \]

### Final Answer
The original coordinates of point P are \((-5, -2)\).

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