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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.

1 answer

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.