The new co-ordinates of the point `(1,1)` when the origin is shifted to the point `(-3,-2)` by translation of axes are .

Answer

To find the new coordinates of the point (1, 1) when the origin is shifted to the point (-3, -2), we can follow these steps:

### Step 1: Understand the Translation of Axes
When the origin is shifted from (0, 0) to a new point (h, k), the new coordinates (X, Y) of any point (x, y) can be calculated using the formulas:
- \( X = x + h \)
- \( Y = y + k \)

### Step 2: Identify the Values
In this case:
- The original point is (x, y) = (1, 1)
- The new origin is (h, k) = (-3, -2)

### Step 3: Substitute the Values into the Formulas
Now we can substitute the values into the equations:
- For X:
\[ X = x + h = 1 + (-3) = 1 - 3 = -2 \]
- For Y:
\[ Y = y + k = 1 + (-2) = 1 - 2 = -1 \]

### Step 4: Write the New Coordinates
Thus, the new coordinates of the point (1, 1) when the origin is shifted to (-3, -2) are:
\[ (X, Y) = (-2, -1) \]

### Final Answer
The new coordinates of the point (1, 1) after the translation of axes are (-2, -1).

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