In the pre-image of the parallelogram, the slope of AD is −3 and the slope of BC is −3. The image is translated down 7 units and then reflected over the y−axis.
The slope of A"D" is .
The slope of B"C" is .
What can you determine about the line segments A"D" and B"C"?

a)The slope of A"D" is 3

The slope of B"C" is 3

b) The line segments A"D" and B"C" are congruent and parallel.

Step-by-step explanation:

The pre-image of the parallelogram, has slope of AD equal −3 and the slope of BC equal −3.

Since translation and reflection are rigid transformations, the preimage and the image are congruent.

This means that the lengths of the corresponding sides are equal.

Hence AD=A"D'' and B"C"=BC

However, since the image after a reflection in the y-axis is laterally inverted, the slope of A"D" will be negative of the slope of AD.

Similarly, the slope of B"C" will be negative of the slope of BC.

The slope of A"D" is 3

The slope of B"C" is 3

Since the two line segments have the same slope, they are parallel.