Find the new co-ordinates of the points :
`(i) (1,1)` `(ii) (5,0)` `(iii) (-2,1)` when the origin is shifted to the point `(-3,-2)` by translation of axes.

Answer

To find the new coordinates of the points when the origin is shifted to the point (-3, -2), we can use the following formula:

If the original coordinates of a point are (x, y) and the new coordinates after shifting the origin to (h, k) are (X, Y), then:

\[ X = x - h \]
\[ Y = y - k \]

Here, \( h = -3 \) and \( k = -2 \).

Now, let's calculate the new coordinates for each of the given points:

### (i) For the point (1, 1):

1. **Original Coordinates**: (x, y) = (1, 1)
2. **Shifted Origin**: (h, k) = (-3, -2)
3. **Calculate New Coordinates**:
- \( X = 1 - (-3) = 1 + 3 = 4 \)
- \( Y = 1 - (-2) = 1 + 2 = 3 \)

**New Coordinates**: (4, 3)

### (ii) For the point (5, 0):

1. **Original Coordinates**: (x, y) = (5, 0)
2. **Shifted Origin**: (h, k) = (-3, -2)
3. **Calculate New Coordinates**:
- \( X = 5 - (-3) = 5 + 3 = 8 \)
- \( Y = 0 - (-2) = 0 + 2 = 2 \)

**New Coordinates**: (8, 2)

### (iii) For the point (-2, 1):

1. **Original Coordinates**: (x, y) = (-2, 1)
2. **Shifted Origin**: (h, k) = (-3, -2)
3. **Calculate New Coordinates**:
- \( X = -2 - (-3) = -2 + 3 = 1 \)
- \( Y = 1 - (-2) = 1 + 2 = 3 \)

**New Coordinates**: (1, 3)

### Summary of New Coordinates:
1. For (1, 1) → (4, 3)
2. For (5, 0) → (8, 2)
3. For (-2, 1) → (1, 3)

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