Best answer gets

what series of transformations would carry trapezoid abcd onto itself?

(x + 0, y − 4), 90° clockwise rotation, reflection over the y-axis

(x + 0, y − 4), 180° rotation, reflection over the y-axis

(x + 6, y + 0), 90° clockwise rotation, reflection over the x‐axis

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Step-by-step explanation:

The answer can be found out simply , a trapezoid has its horizontal sides usually parallel meanwhile the vertical sides are not parallel.

The horizontal parallel sides are on the x-axis.

Reflection over y- axis would leave the trapezoid in a vertical position such that the trapezoid ABCD won't be carried on the transformed trapezoid as shown in figure.

So option 1 and 2 are removed.

Now, a 90 degree rotation would leave the trapezoid in a vertical position again so its not suitable again.

In,The final option (x + 6, y + 0), 180° rotation, reflection over the x‐axis, x+6 would allow the parallel sides to increase in value hence the trapezoid would increase in size,

180 degree rotation would leave the trapezoid in an opposite position and reflection over x-axis would bring it below the Original trapezoid. Hence, transformed trapezoid A`B`C`D` would carry original trapezoid ABCD onto itself

check out this website

you will enjoy it as it give interesting things to look up or do!