Question

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

Explanation:

Step1: Recall transformation rules

Reflection across x - axis changes (x,y) to (x, - y). Reflection across y - axis changes (x,y) to (-x,y). Translation right 1 unit changes (x,y) to (x + 1,y) and translation left 1 unit changes (x,y) to (x - 1,y).

Step2: Analyze the first option

If we reflect △ABC across the x - axis, then translate right 1 unit. Let a vertex of △ABC be (x,y). After reflection across x - axis, it becomes (x, - y). After translation right 1 unit, it becomes (x + 1,-y).

Step3: Analyze the second option

If we reflect △ABC across the y - axis, then translate right 1 unit. A vertex (x,y) of △ABC becomes (-x,y) after reflection across y - axis and (-x + 1,y) after translation right 1 unit.

Step4: Analyze the third option

If we reflect △ABC across the x - axis, then translate left 1 unit. A vertex (x,y) of △ABC becomes (x, - y) after reflection across x - axis and (x-1,-y) after translation left 1 unit.

Step5: Analyze the fourth option

If we reflect △ABC across the y - axis, then translate left 1 unit. A vertex (x,y) of △ABC becomes (-x,y) after reflection across y - axis and (-x - 1,y) after translation left 1 unit.
We need to find the sequence that maps △ABC to △DEF. By observing the orientation and position of the triangles on the coordinate - grid, if we reflect △ABC across the x - axis (flips it over the x - axis) and then translate it right 1 unit, we can get △DEF.

Answer:

Reflect △ABC across the x - axis, then translate it right 1.