Question

two triangles are shown on the coordinate grid. △abc≅△def. which sequence of transformations shows that reflect △abc across the x - axis, then translate it down 1 reflect △abc across the x - axis, then translate it up 1 reflect △abc across the y - axis, then translate it down 1 reflect △abc across the y - axis, then translate it up 1

Explanation:

Step1: Recall transformation rules

Reflection across x - axis changes (x,y) to (x, - y). Translation down 1 unit changes (x,y) to (x,y - 1).

Step2: Analyze each option

For option 1: Reflecting △ABC across the x - axis changes the y - coordinates of its vertices to their opposites. Then translating it down 1 unit subtracts 1 from the new y - coordinates. This sequence of transformations can map △ABC to △DEF.
For option 2: Reflecting across x - axis and then translating up 1 unit will not map △ABC to △DEF as the vertical position after translation is wrong.
For option 3: Reflecting across y - axis changes (x,y) to (-x,y) and then translating down 1 unit. This will not map △ABC to △DEF as the horizontal position after reflection is wrong.
For option 4: Reflecting across y - axis and then translating up 1 unit will not map △ABC to △DEF due to wrong horizontal and vertical positions after transformation.

Answer:

The first option: Reflect △ABC across the x - axis, then translate it down 1.