Use the image to answer the question.

Question

A coordinate plane shows two rectangles A B C D and A double dash B double dash C double dash D double dash. Both the axes range from negative 5 to 5 in unit increments.

Identify a sequence of rigid transformations that would map ABCD→A"B"C"D" . Give your answer in the form of a composition transformation mapping.

(1 point)
Responses

(x,y)→(−x,y−4)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y minus 4 right parenthesis

(x,y)→(−x−4,y)
left parenthesis x comma y right parenthesis right arrow left parenthesis negative x minus 4 comma y right parenthesis

(x,y)→(x,y+4)
left parenthesis x comma y right parenthesis right arrow left parenthesis x comma y plus 4 right parenthesis

(x,y)→(x,−y−4)

Answer 1

To determine the appropriate sequence of rigid transformations that maps rectangle ABCD to rectangle A"B"C"D", we need to analyze the transformations involved.

1. Reflection: The transformation might involve reflecting the points across a vertical line, which would imply a transformation of the form (x, y) → (-x, y).

2. Translation: After reflection, the rectangle might be translated upwards or downwards. It seems from the problem that the rectangle A"B"C"D" is shifted compared to ABCD.

Given the options provided, we look for a combination of these transformations.

The provided options include:

• (x,y)→(−x,y−4)
• (x,y)→(−x−4,y)
• (x,y)→(x,y+4)
• (x,y)→(x,−y−4)

From examining these options, the transformation that makes sense for a reflection followed by a vertical translation appears to be:

\((x,y)→(−x,y−4)\)

This transformation reflects the points across the y-axis (negating the x-coordinate) and then translates the resulting points 4 units down (subtracting 4 from the y-coordinate).

In conclusion, the composition transformation mapping is:

\[ (x,y)→(−x,y−4) \]