Question

What series of transformations would carry parallelogram ABCD onto itself?

Answer 1

THE answer is c (x + 6, y + 0), 180° rotation, (x + 0, y + 4)

Explanation:

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Answer 2

C. (x+6,y+0), 180° rotation, (x+0,y+4)

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.