If the point (3,-2) is transformed to (-2,1) which the origin is shifted to P, then P=

Answer

To find the coordinates of the new origin \( P \) after the point \( (3, -2) \) is transformed to \( (-2, 1) \), we can use the translation of axes formula. Here’s a step-by-step solution:

### Step 1: Understand the transformation
We have the original point \( (3, -2) \) and it transforms to the new point \( (-2, 1) \). We need to find the coordinates of the new origin \( P \) which we will denote as \( (H, K) \).

### Step 2: Set up the equations
Using the translation of axes formula:
\[ X = x - H \]
\[ Y = y - K \]
where \( (x, y) \) are the coordinates of the point in the old coordinate system and \( (X, Y) \) are the coordinates in the new coordinate system.

### Step 3: Substitute the known values
From the problem:
- Old point \( (x, y) = (3, -2) \)
- New point \( (X, Y) = (-2, 1) \)

Substituting these values into the equations:
1. For the x-coordinates:
\[ -2 = 3 - H \]
2. For the y-coordinates:
\[ 1 = -2 - K \]

### Step 4: Solve for \( H \)
From the first equation:
\[ -2 = 3 - H \]
Rearranging gives:
\[ H = 3 + 2 = 5 \]

### Step 5: Solve for \( K \)
From the second equation:
\[ 1 = -2 - K \]
Rearranging gives:
\[ K = -2 - 1 = -3 \]

### Step 6: Write the coordinates of the new origin
Thus, the coordinates of the new origin \( P \) are:
\[ P = (H, K) = (5, -3) \]

### Final Answer
The coordinates of the new origin \( P \) are \( (5, -3) \).

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