Transformations Online Practice

Question

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Question
Use the images to answer the question.

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

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

(1 point)
Responses

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 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 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.

Answer 1

To determine the correct depiction of rectangle A′B′D′C′ after the specified translations, we need to understand the transformations applied to the rectangle ABDC.

1. Translation: A translation by -1 horizontally means that each vertex will move 1 unit to the left. A translation by -3 vertically means that each vertex will move 3 units down.

2. Vertices Adjustment:

   • If the original vertices are:
     • A (x, y)
     • B (x+width, y)
     • C (x+width, y+height)
     • D (x, y+height)
   • After translating:
     • A′ (x - 1, y - 3)
     • B′ (x + width - 1, y - 3)
     • C′ (x + width - 1, y + height - 3)
     • D′ (x - 1, y + height - 3)

3. Selection of the Image: To accurately answer which rectangle corresponds to the new vertices A′B′D′C′, we would look for the following characteristics in the provided images:

• Each vertex should reflect the correct movement resulting from the translations.
• The shaded area should still represent a rectangle, just shifted.

Without explicit coordinates or images, I can't select the correct image directly, but follow the translation process described to identify which one matches the resulting vertices of rectangle A'B'D'C'.

If you observe the coordinates marked in each image, apply the transformations as described and look for the rectangle that reflects those new coordinates (A', B', C', D').