Question

If rectangle ABDC is translated horizontally −1 and vertically +3, which of the following correctly depicts rectangle A′B′D′C′ ?

Answer 1

The original coordinates are, A is, (-5,4) B is, (-1,4) C is, (-5,1) D is, (-1,1)

Answer 2

To find the new coordinates of rectangle ABDC after the translation, we need to apply the given transformations: a horizontal translation of -1 (which means we move left by 1 unit) and a vertical translation of +3 (which means we move up by 3 units).

Let’s assume the original coordinates of the rectangle ABDC are:
- A(x1, y1)
- B(x2, y1)
- D(x1, y2)
- C(x2, y2)

After applying the transformations:
- For point A (x1, y1):
- New A' = A'(x1 - 1, y1 + 3)
- For point B (x2, y1):
- New B' = B'(x2 - 1, y1 + 3)
- For point D (x1, y2):
- New D' = D'(x1 - 1, y2 + 3)
- For point C (x2, y2):
- New C' = C'(x2 - 1, y2 + 3)

In summary, after the translation, the new coordinates will be:
- A' = (x1 - 1, y1 + 3)
- B' = (x2 - 1, y1 + 3)
- D' = (x1 - 1, y2 + 3)
- C' = (x2 - 1, y2 + 3)

To identify which depiction correctly represents rectangle A′B′D′C′, you would need to look for a rectangle that has these transformed coordinates based on your specific original coordinates for ABDC. If you have a visual representation or specific coordinates, please provide those so I can help you identify the correct depiction!

Answer 3

Given the original coordinates of rectangle ABDC:

- A (-5, 4)
- B (-1, 4)
- C (-5, 1)
- D (-1, 1)

We will translate these points with the transformations: a horizontal translation of -1 (to the left) and a vertical translation of +3 (upward).

### Applying the translations:

1. **Point A (-5, 4)**:
- New A' = (-5 - 1, 4 + 3) = (-6, 7)

2. **Point B (-1, 4)**:
- New B' = (-1 - 1, 4 + 3) = (-2, 7)

3. **Point D (-1, 1)**:
- New D' = (-1 - 1, 1 + 3) = (-2, 4)

4. **Point C (-5, 1)**:
- New C' = (-5 - 1, 1 + 3) = (-6, 4)

### New Coordinates of A′B′D′C′:
- A′ = (-6, 7)
- B′ = (-2, 7)
- C′ = (-6, 4)
- D′ = (-2, 4)

### Characteristics of Rectangle A'B'D'C':
- The x-coordinates of A' and C' are the same (-6), and the x-coordinates of B' and D' are the same (-2).
- The y-coordinates of A' and B' are the same (7), and the y-coordinates of C' and D' are the same (4).

### Conclusion:
So, rectangle A′B′D′C′ will have the vertices:
- A′ (-6, 7)
- B′ (-2, 7)
- C′ (-6, 4)
- D′ (-2, 4)

Look for a visual representation or a description that resembles these points to identify the correct depiction of rectangle A′B′D′C′.