Question

If rectangle ABDC (coordinates; A(-5, 4), B(-1, 4), C(-5, 1), D(-1, 1) ) is translated horizontally −1 and vertically +3, which of the following correctly depicts rectangle A′B′D′C′ ?

Answer 1

To translate the rectangle \( ABDC \) horizontally \( -1 \) (to the left) and vertically \( +3 \) (upwards), we need to apply the translation to each point of the rectangle.

The translation can be represented as:
- New x-coordinate = Original x-coordinate - 1
- New y-coordinate = Original y-coordinate + 3

Now, let's apply this translation to each vertex:

1. **Point A**:
- Original coordinates: \( A(-5, 4) \)
- Translated coordinates: \( A'(-5 - 1, 4 + 3) = A'(-6, 7) \)

2. **Point B**:
- Original coordinates: \( B(-1, 4) \)
- Translated coordinates: \( B'(-1 - 1, 4 + 3) = B'(-2, 7) \)

3. **Point D**:
- Original coordinates: \( D(-1, 1) \)
- Translated coordinates: \( D'(-1 - 1, 1 + 3) = D'(-2, 4) \)

4. **Point C**:
- Original coordinates: \( C(-5, 1) \)
- Translated coordinates: \( C'(-5 - 1, 1 + 3) = C'(-6, 4) \)

Therefore, the new coordinates for the vertices of rectangle \( A'B'D'C' \) after the translation are:
- \( A'(-6, 7) \)
- \( B'(-2, 7) \)
- \( C'(-6, 4) \)
- \( D'(-2, 4) \)

So the rectangle \( A'B'D'C' \) will have its vertices at these new coordinates.