Question

Figure 1 and Figure 2 are two congruent parallelograms drawn on a coordinate grid as shown. Which two transformations can map Figure 1 onto Figure 2?

reflection across the x-axis followed by reflection across y-axis

reflection across the y-axis followed by reflection across x-axis

reflection across the y-axis followed by translation 5 units down

reflection across the y-axis followed by translation 10 units down

Answer 1

Reflection across y-axis followed by translation 10 units down.

The coordinates of figure 1 are: (-4,8), (-6,6), (-5,3), (-3,5)

To reflect across the y-axis, replace the x coordinates of figure 1 with -x.

So the reflected coordinates across the y-axis for figure 1 are: (4,8), (6,6),(5,3), (3,5)

A translation of 10 units down means you subtract 10 from the y coordinate of figure 1. Since we have reflected figure 1 across the y-axis in the previous step, then we will subtract 10 from those reflected coordinates.

So coordinate (4,8) becomes (4,-2), coordinate (6,6) becomes (6,-4), coordinate (5,3) becomes (5,-7) and coordinate (3,5) becomes (3,-5)