Answer:
The translation rule will be: (x, y) → (x+3, y+9)
Explanation:
As X'Y' is a translation of XY.
As the location of the vertix X is (-4, -9) and the coordinates of vertex Y is (-5, -5).
As X'Y' be the vertices of the translated figure.
So, if we translate the segment XY +3 units in the x-direction and +9 units in the y-direction, i.e.
(x, y) → (x+3, y+9) = (-4+3, -9+9) = (-1, 0) = X'
and
(x, y) → (x+3, y+9) = (-5+3, -5+9) = (-2, 4) = Y'
so, the image X'Y' will have the X' vertice at the location (-1, 0) and Y' vertice at the location (-2, 4).
Therefore, the translation rule will be: (x, y) → (x+3, y+9)