To determine the correct depiction of rectangle A'B'D'C' after a translation of rectangle ABDC horizontally by -1 and vertically by +3, we need to analyze the translations:
- Horizontal Translation: A movement of -1 means each x-coordinate of the vertices is decreased by 1.
- Vertical Translation: A movement of +3 means each y-coordinate of the vertices is increased by 3.
If we have the original coordinates of rectangle ABDC as:
- A (x1, y1)
- B (x2, y2)
- C (x3, y3)
- D (x4, y4)
After the transformations, the new coordinates would be:
- A' (x1 - 1, y1 + 3)
- B' (x2 - 1, y2 + 3)
- C' (x3 - 1, y3 + 3)
- D' (x4 - 1, y4 + 3)
Now, we need to look for a depiction of rectangle A'B'D'C' that shows it with these new coordinates. The options suggest different arrangements and data labeling.
Here’s how to assess each option:
A. This option depicts a quadrilateral with coordinates but does not specifically point out that it's shaded or provide a rectangle shape.
B. This option only mentions that a rectangle is formed by connecting four data points, lacking shading and labeling that could help confirm it's A'B'D'C'.
C. This option describes a rectangle that is shaded with labeled vertices but does not provide coordinates, which are important for verifying the translation.
D. This option describes a shaded rectangle with labeled vertices and specifically mentions that those vertices are marked with coordinates. This is the most detailed option, ensuring that the shape is correct, shaded, and easy to understand with exact coordinates.
Therefore, the best choice is:
D. 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.