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 minus y negative 4 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
The correct answer is:
(x,y)→(x,y+4)
To identify a sequence of rigid transformations, we need to analyze the given points and determine the transformations needed to map them to the new points A', B', C', and D'.
Let's go through each point and compare the coordinates:
A: (x, y) → A': (−x, y−4)
B: (x, y) → B': (−x−4, y)
C: (x, y) → C': (x, −y−4)
D: (x, y) → D': (x, y+4)
From the given transformations, we can see that:
1. For A, the point is reflected across the y-axis (−x) and shifted down by 4 units in the y-direction (y−4).
2. For B, the point is reflected across the y-axis (−x) and shifted left by 4 units in the x-direction (−x−4).
3. For C, the point is shifted down by 4 units in the y-direction (−y−4).
4. For D, the point is shifted up by 4 units in the y-direction (y+4).
Now, let's write the composition transformation mapping:
1. Reflect across the y-axis: (x, y) → (−x, y)
2. Shift down by 4 units in the y-direction: (x, y) → (x, y−4)
3. Shift left by 4 units in the x-direction: (x, y) → (x−4, y)
4. Shift down by 4 units in the y-direction: (x, y) → (x, y−4)
5. Shift left by 4 units in the x-direction: (x, y) → (x−4, y)
Thus, the sequence of rigid transformations that would map ABCD to A'B'C'D' is:
1. Reflect across the y-axis
2. Shift down by 4 units in the y-direction
3. Shift left by 4 units in the x-direction
4. Shift down by 4 units in the y-direction
5. Shift left by 4 units in the x-direction