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

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.
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1 answer

To determine the correct depiction of rectangle A'B'D'C' after translating rectangle ABCD horizontally by -1 and vertically by +3, we need to apply the transformation to the coordinates of each vertex of rectangle ABCD.

Let's assume the coordinates of the rectangle ABCD are as follows:

  • A (x1, y1)
  • B (x2, y1)
  • C (x2, y2)
  • D (x1, y2)

After applying the transformations:

  1. Horizontal translation by -1: This means we subtract 1 from the x-coordinates.
  2. Vertical translation by +3: This means we add 3 to the y-coordinates.

Therefore, the new coordinates will be:

  • A' (x1 - 1, y1 + 3)
  • B' (x2 - 1, y1 + 3)
  • C' (x2 - 1, y2 + 3)
  • D' (x1 - 1, y2 + 3)

Now, we need to see which of the given options corresponds to these new vertices (A', B', C', D').

Since I don't have access to the actual images, you should compare the options based on the coordinates of the rectangles listed for A', B', D', C' with what we derived here. Look for the image that:

  • Shows a rectangle labeled A'B'D'C' with the new coordinates correctly positioned after the translation.

One of the options should depict the rectangle fitting these criteria.