Pentagon abcde and pentagon a'b'c'd'e' are shown on the coordinate plane below:
which two transformations are applied to pentagon abcde to create a'b'c'd'e'?
translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the x-axis
translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the y-axis
translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the y-axis
translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the x-axis

translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the x-axis

Reasoning:

1) The translation options are x + 8 or x + 2 and y + 2 or y + 8.

That means that the points are translated to the right and upward.

2) Then, you need to rotate the figure over the x-axis to translate it to the fourth quadrant.

To find the answer you can choose just one point to verify the rule.

3) Using the point D (-2,2) which is translated to D' (6, - 4) and knowing that the rotation over the x-axis keeps the x-coordinate unchanged while the y-coordinate is transformed into its negative, you can conclude that

3a) first the point was translated 8 units to the right and two units upward this is to a poin with x-coordinate  -2 + 8 = 6 and y-coordinate 2 + 2 = 4

3b) second the point was reflected over the x -axis keeping the same x-coordinate  x = 6 and transforming the y-coordinate into y = - 4.

So, the rule has been discovered: (x, y) →(x + 8, y + 2) and reflected across the x-axis

Here are the answers to the ones that i could see.