Answer:
(x + 0, y − 4), 180° rotation, reflection over the y-axis (A)
Step-by-step explanation:
(x + 0, y − 4), 180° rotation, reflection over the y-axis Is right because i got it right on my test. Option A. Check your options because they could be mixed up so don't rely on the answer choice look at the actual answer.
Transformation involves changing the position of a shape.
The series of transformation that carries the ABCD onto itself is: (A) (x + 0, y − 4), 180° rotation, reflection over the y-axis
The coordinates of the rectangle are:
[tex]A = (-5,1)[/tex]
[tex]B = (-5,3)[/tex]
[tex]C = (-1,3)[/tex]
[tex]D = (-1,1)[/tex]
Next, we test the options.
A. (x + 0, y − 4), 180° rotation, reflection over the y-axis
Apply translation (x + 0, y − 4) on ABCD
[tex]A' = (-5 + 0, 1 - 4)[/tex]
[tex]A= (-5,-3)[/tex]
[tex]B' = (-5 + 0, 3 - 4)[/tex]
[tex]B' = (-5, - 1)[/tex]
[tex]C' = (-1+0, 3 - 4)[/tex]
[tex]C' = (-1, - 1)[/tex]
[tex]D' = (-1 + 0, 1 - 4)[/tex]
[tex]D' = (-1, - 3)[/tex]
Rotate by 180 degrees
The rule of this transformation is: (x,y)→(−x,−y)
So, we have:
[tex]A" = (5,3)[/tex]
[tex]B" = (5,1)[/tex]
[tex]C" = (1,1)[/tex]
[tex]D" = (1,3)[/tex]
Lastly, reflect over the y-axis
The rule of this transformation is: (x,y)→(−x,y)
So, we have:
[tex]A"' = (-5,3)[/tex]
[tex]B"' = (-5,1)[/tex]
[tex]C"' = (-1,1)[/tex]
[tex]D"' = (-1,3)[/tex]
Now, compare the coordinates of ABCD and (ABCD)"'
By comparison, we have:
[tex]A = (-5,1)[/tex] => [tex]B"' = (-5,1)[/tex]
[tex]B = (-5,3)[/tex] => [tex]A"' = (-5,3)[/tex]
[tex]C = (-1,3)[/tex] => [tex]C"' = (-1,1)[/tex]
[tex]D = (-1,1)[/tex] => [tex]D"' = (-1,3)[/tex]
The above means that, the transformation carries the rectangle onto itself, because the image of the rectangle and the original rectangle have the same coordinates.
Hence, (a) is true
Read more about transformations at:
https://brainly.com/question/11707700
