Question

I need it now a reflection across the y-axis followed by a reflection across the x-axis maps parallelogram ABCD onto parallelogram A'B'C'D'.

Select all of the true statements.

Answer 1

true statements:

- A'B' is parallel to C'D'

- the area of parallelogram ABCD is equal to area of A'B'C'D'

- the perimeter of ABCD is equal to the perimeter of A'B'C'D'

btw just so u understand the work i have shown above:

- the green parallelogram is the original one before any work was done

- the blue one was after it was reflected across the y-axis

- and the brown one was after the blue parallelogram was reflected across the x-axis

sorry if that was a confusion... i forgot to add it above im really sorry

but apart from that, hope u understand and get an A :))

Answer 2

When parallelogram ABCD is successively reflected across the y-axis and x-axis, it returns to its original position. Therefore, the area and perimeter of ABCD are equal to those of A'B'C'D'. Here all options are correct.

When a figure is reflected across an axis, the image is the same as the original figure, but flipped across the axis. So, when parallelogram ABCD is reflected across the y-axis, the resulting figure, A'B'C'D', is the same as ABCD, but flipped horizontally.

When A'B'C'D' is then reflected across the x-axis, the resulting figure is ABCD. This is because a reflection across the x-axis flips a figure vertically, so it undoes the previous reflection across the y-axis.

Since the area of a figure is calculated by multiplying its base by its height, and reflections do not change the distances between points, the area of ABCD will be the same as the area of A'B'C'D'.

Similarly, the perimeter of a figure is the sum of the lengths of its sides, and reflections do not change the distances between points, so the perimeter of ABCD will be the same as the perimeter of A'B'C'D'. Here all options are correct.