The image of trapezoid ABCD has coordinates A'(-2,-5), B'(-1,-2), C'(2,-2), and D'(3,-5). It was translated by the rule T_1, -3(x, y). Which diagram shows the pre-image?

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

38 was the other number of your question.

3 4 7 12 19

+1 +3 +5 +6

i would guess 26 because this isnt a sequential pattern or its to short to know