The origin is shifted to (-2,3) then what are the co-ordinates of the point (3,-5) in the new position ?

Answer

To find the new coordinates of the point (3, -5) after shifting the origin to (-2, 3), we can follow these steps:

### Step 1: Identify the original coordinates of the point
The original coordinates of the point are given as:
- \( P(x, y) = (3, -5) \)

### Step 2: Identify the new origin
The new origin is given as:
- \( O(\alpha, \beta) = (-2, 3) \)

### Step 3: Determine the new coordinates
To find the new coordinates \( P'(x', y') \) of point \( P \) with respect to the new origin, we use the formulas:
- \( x' = x - \alpha \)
- \( y' = y - \beta \)

### Step 4: Substitute the values into the formulas
Substituting the values into the formulas:
- For \( x' \):
\[ x' = 3 - (-2) = 3 + 2 = 5 \]

- For \( y' \):
\[ y' = -5 - 3 = -8 \]

### Step 5: Write the new coordinates
Thus, the new coordinates of the point \( P \) with respect to the new origin are:
- \( P'(x', y') = (5, -8) \)

### Final Answer
The coordinates of the point (3, -5) in the new position are \( (5, -8) \).

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