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.
Possible Answers:
(x,y)→(x+4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis (x,y)→(x,−y−4) open paren x comma y close paren rightarrow open paren x comma negative y minus 4 close paren (x,y)→(x−4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x minus 4 comma negative y right parenthesis (x,y)→(x,−y+4)

Answer 1

To determine the appropriate sequence of transformations that maps triangle ABCD to A"B"C"D", we need to consider what kind of transformations are needed—translations, reflections, or rotations.

Let's analyze the transformations given in the options:

- **(x, y) → (x + 4, -y)**: This transformation shifts all points 4 units to the right and reflects the y-coordinates, which means it flips the figure over the x-axis.

- **(x, y) → (x, -y - 4)**: This transformation reflects the y-coordinates and then shifts them down 4 units.

- **(x, y) → (x - 4, -y)**: This transformation shifts all points 4 units to the left and reflects the y-coordinates.

- **(x, y) → (x, -y + 4)**: This transformation reflects the y-coordinates and then shifts them up 4 units.

To find the correct composition transformation, we consider the target coordinates of A"B"C"D" relative to ABCD. We should assess whether we need vertical flips and horizontal shifts based on the relationships between corresponding points.

From the transformations, if we assume that A"B"C"D" needs a horizontal shift to the right and a vertical reflection, the most suitable option would be:

**(x, y) → (x + 4, -y)**

This maps points to the right by 4 units and reflects them across the x-axis, making it a likely candidate.

Thus, the answer is:

**(x, y) → (x + 4, -y)**.