what series of transformations would carry parallelogram ABCD onto itself?

Accepted Solution

Answer:C. (x+6,y+0), 180Β° 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), thenA'(1,1)B'(2,3)C'(5,3)D'(4,1)2. 180Β° rotation has the rule(x,y)β†’(-x,-y).ThenA'(1,1)β†’A''(-1,-1)B'(2,3)β†’B''(-2,-3)C'(5,3)β†’C''(-5,-3)D'(4,1)β†’D''(-4,-1)3. Translation (x+0,y+4) maps points A'', B'', C'' and D'' into points A''(-1,-1)β†’C(-1,3)B''(-2,-3)β†’D(-2,1)C''(-5,-3)β†’A(-5,1)D''(-4,-1)β†’B(-4,3)So, the image of the parallelogram ABCD after these three transformation will coincide with the initial parallelogram.