Answer:
C. (x+6,y+0), 180° rotation, (x+0,y+4)
Step-by-step explanation:
Parallelogram ABCD has vertices at points A(-5,1), B(-4,3), C(-1,3) and D(-2,1).
1. Translation with the rule (x+6,y+0), then
- A'(1,1)
- B'(2,3)
- C'(5,3)
- D'(4,1)
2. 180° rotation has the rule
(x,y)→(-x,-y).
Then
- A'(1,1)→A''(-1,-1)
- B'(2,3)→B''(-2,-3)
- C'(5,3)→C''(-5,-3)
- D'(4,1)→D''(-4,-1)
3. Translation (x+0,y+4) maps points A'', B'', C'' and D'' into points
- A''(-1,-1)→C(-1,3)
- B''(-2,-3)→D(-2,1)
- C''(-5,-3)→A(-5,1)
- D''(-4,-1)→B(-4,3)
So, the image of the parallelogram ABCD after these three transformation will coincide with the initial parallelogram.
