Question

What image is the translation of abc given by the translation rule (x y) (x+2 y-2)

Answer 1

The third picture you attached where the translated triangle is down to the right of the original would be the translation given the rule (x, y) (x+2, y-2) because it has been translated 2 units in the positive direction of the x axis (right) and 2 units in the negative direction of the y axis (down).

Answer 2

we know that

The rule of the translation is

$(x,y)---------> (x+2,y-2)$

That means

The translation is $2$ units to the right and  $2$ units down

therefore

the answer in the attached figure