Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below. Which two transformations can map figure 1 onto figure 2?
Reflection across the y-axis, followed by translation 10 units down
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 x-axis, followed by reflection across y-axis

Solution:

From the figure1,

The vertices are (-3, 4); (-4, 7); (-5, 2); (-6, 5)

From the figure 2,

The vertices are (7, -4); (6, -7); (5, -2); (4, -5)

Since, many sets of two transformations can transform the figure 1 into the figure 2, we need to probe each pair of the choice statements.

From option 1

A reflection across the x-axis, keeps the x-coordinate and change the y-coordinate to its opposite(negative), i.e.(x, y) to (x, -y)

Now figure1 becomes,

(-3, 4) to (-3, -4)

(-4, 7) to (-4, -7)

(-5, 2) to (-5, -2)

(-6, 5) to (-6, -5)

From option 2

A translation of 10 units transforms the points (x, y) to (x+10, y)

(-3, 4) to (-3 + 10, -4) = (7, -4)

(-4, 7) to (-4 + 10, -7) = (6, -7)

(-5, 2) to (-5 + 10, -2) = (5, -2)

(-6, 5) to (-6 + 10, -5) = (4, -5)

Therefore, it can be proved that the two transformations given in the option A transforms figure 1 into figure 2.

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

Summary:

Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid. The two transformations that can map figure 1 onto figure 2 is the reflection across the x-axis, followed by translation 10 units down.