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? select one: a. reflection across the y-axis, followed by reflection across x-axis b. reflection across the x-axis, followed by reflection across y-axis c. reflection across the x-axis, followed by translation 10 units right d. reflection across the y-axis, followed by translation 5 units down

I found the figure and take advantage to attache it for any reference.

c. Reflection across the x-axis, followed by translation 10 units right 
Explanation:

1) The vertices of figure 1 are: (-3, 4); (-4, 7); (-5, 2); (-6, 5)

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

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

4) This proves that the statements of the option C. yield the figure 2:

1) Reflection across the x-axis.

A reflection across the x-axis, keeps the x-coordinate, and change the y-coordinate to its opposite (negative). This is: (x, y) → (x - y).

Use that rule on the 4 vertices of the figure 1 and you get:

(-3, 4) → (-3, -4);
(-4, 7) → (-4, -7);
(-5, 2) → (-5, -2);
(-6, 5) → (-6, -5)

2) Translation 10 units right

A translation of 10 units transforms the points (x,y) into (x + 10, y): (x,y) → (x + 10), y)

Apply that rule:
(-3, -4) → (-3 + 10, -4) = (7, -4)

(-4, -7) → (-4 + 10, 7) = (6, -7)

(-5, -2) → (-5 + 10, -2) = (5, -2)
(-6, -5) → (-6 + 10, -5) = (4, - 5)

Then, it has been proven that the two transformations given in the option C. transforms figure 1 onto figure 2.

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