Use the image to answer the question. 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−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) left parenthesis x comma y right parenthesis right arrow left parenthesis x comma minus y negative 4 right parenthesis (x,y)→(−x,y−4) left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y minus 4 right parenthesis Skip to navigation page 14 of 14

1 answer

To determine the sequence of rigid transformations that maps \( ABCD \) to \( A"B"C"D" \), we need to analyze the types of transformations:

  1. Reflection: This transformation flips the shape over a line.
  2. Translation: This shifts the shape without changing its orientation.
  3. Rotation: This turns the shape around a point by a certain angle.

Without the image, I can guide you through the thought process:

  1. Reflection: Check if there is a reflection across either the x-axis, y-axis, or some line that might map A to A" (similarly for B, C, D).

  2. Translation: If the shape is the same, but in a different position, this requires shifting it by specific amounts horizontally or vertically.

  3. Combination: Sometimes, a combination of transformations, like reflecting followed by translating, might be necessary.

Given the options you provided, analyze each transformation's effect on the points:

  • (x,y) → (−x−4,y): This performs a reflection across the y-axis and then translates left by 4.

  • (x,y) → (x,y+4): This just translates up by 4.

  • (x,y) → (x,−y−4): This reflects across the x-axis and translates down by 4.

  • (x,y) → (−x,y−4): This reflects across the y-axis and translates down by 4.

Select the option that matches the transformation from \( ABCD \) to \( A"B"C"D" \). Look for evidence of vertical/horizontal shifts and whether reflection occurred.

If you can provide more details or context from the image, I would be able to help identify the specific transformation more precisely.