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.
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.
Answers
GPT-4o mini
To determine the resulting coordinates of rectangle \( A'B'D'C' \) after the translation of rectangle \( ABDC \), we need to apply the specified transformations to the coordinates of the original vertices.
The translation is described as moving horizontally by \(-1\) (which means moving left by 1 unit) and vertically by \(-3\) (which means moving down by 3 units).
If we denote the coordinates of the vertices of rectangle \( ABDC \) as follows:
- \( A(x_A, y_A) \)
- \( B(x_B, y_B) \)
- \( D(x_D, y_D) \)
- \( C(x_C, y_C) \)
After the translations, the new coordinates \( A', B', D', C' \) are given by:
- \( A'(x_A - 1, y_A - 3) \)
- \( B'(x_B - 1, y_B - 3) \)
- \( D'(x_D - 1, y_D - 3) \)
- \( C'(x_C - 1, y_C - 3) \)
With the image representations you described, to select the correct depiction, look for the rectangle \( A'B'D'C' \) where each vertex has been correctly transformed according to the specified translation.
Please choose the image that correctly shows the translated positions of the vertices \( A', B', D', \) and \( C' \). If any of the options displayed the vertices with their new transformed coordinates accurately reflecting the \((-1, -3)\) translation, that would be the correct choice.
The translation is described as moving horizontally by \(-1\) (which means moving left by 1 unit) and vertically by \(-3\) (which means moving down by 3 units).
If we denote the coordinates of the vertices of rectangle \( ABDC \) as follows:
- \( A(x_A, y_A) \)
- \( B(x_B, y_B) \)
- \( D(x_D, y_D) \)
- \( C(x_C, y_C) \)
After the translations, the new coordinates \( A', B', D', C' \) are given by:
- \( A'(x_A - 1, y_A - 3) \)
- \( B'(x_B - 1, y_B - 3) \)
- \( D'(x_D - 1, y_D - 3) \)
- \( C'(x_C - 1, y_C - 3) \)
With the image representations you described, to select the correct depiction, look for the rectangle \( A'B'D'C' \) where each vertex has been correctly transformed according to the specified translation.
Please choose the image that correctly shows the translated positions of the vertices \( A', B', D', \) and \( C' \). If any of the options displayed the vertices with their new transformed coordinates accurately reflecting the \((-1, -3)\) translation, that would be the correct choice.