Question

Use the images to answer the question.

A rectangle is labeled upper A upper B upper C upper D. The area inside of the rectangle is shaded, and each of the vertices is labeled.

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

(1 point)
Responses

A quadrilateral is labeled upper A prime upper B prime upper D prime upper C prime. Each of the four corners of the shape are labeled with the coordinates.
Image with alt text: A quadrilateral is labeled upper A prime upper B prime upper D prime upper C prime. Each of the four corners of the shape are labeled with the coordinates.

A rectangle is labeled upper A prime upper B prime upper D prime upper C prime. The area inside of the rectangle is shaded, and each of the vertices is labeled.
Image with alt text: A rectangle is labeled upper A prime upper B prime upper D prime upper C prime. The area inside of the rectangle is shaded, and each of the vertices is labeled.

A rectangle is labeled upper A prime upper B prime upper D prime upper C prime. The area inside of the rectangle is shaded, and each of the vertices is marked with coordinates.
Image with alt text: A rectangle is labeled upper A prime upper B prime upper D prime upper C prime. The area inside of the rectangle is shaded, and each of the vertices is marked with coordinates.

A rectangle is formed by connecting four data points.
Image with alt text: A rectangle is formed by connecting four data points.

Answer 1

To determine which option correctly depicts rectangle A′B′C′D′ after it has been translated horizontally −1 unit and vertically +3 units, we need to analyze the movement of the rectangle.

1. **Translation**:
- Horizontal translation of -1 means we move the rectangle 1 unit left.
- Vertical translation of +3 means we move the rectangle 3 units up.

If we begin with the original coordinates of rectangle ABCD (let’s denote them as \( A(x_1, y_1) \), \( B(x_2, y_1) \), \( C(x_2, y_2) \), \( D(x_1, y_2) \)), the new coordinates for A′B′C′D′ will be:
- \( A'(x_1 - 1, y_1 + 3) \)
- \( B'(x_2 - 1, y_1 + 3) \)
- \( C'(x_2 - 1, y_2 + 3) \)
- \( D'(x_1 - 1, y_2 + 3) \)

Now, using this translation, we can determine which of the provided options depicts rectangle A′B′C′D′ accurately:

**Responses Evaluation**:
1. **Option 1**: A quadrilateral is labeled A′B′D′C′ only showing coordinates.
- This option does not represent the translated rectangle as a complete shape with all vertices shown.

2. **Option 2**: A rectangle labeled A′B′D′C′ with a shaded area is illustrated.
- This option could potentially match, but the description needs to confirm the coordinates of vertices to validate it.

3. **Option 3**: A rectangle labeled A′B′D′C′ with a shaded area and marked coordinates.
- This option would provide coordinates and shading that signify a translation, which would include verification of the 1 unit left and 3 units up.

4. **Option 4**: A rectangle formed by connecting four data points.
- This is vague and doesn’t provide information explicitly about coordinates or shading patterns that indicate the transformation.

Without specific coordinates being provided, the best option would likely be **Option 3** since it combines visibility of the shape, shading, and clarity with marked coordinates confirming the correct position after translation.

Therefore, I would select **Option 3** as the best representation.