Let in the triangle ABC, vertex A(x1,y1), vertex B(x2,y2) and vertex C(x3,y3)
after translation of (x + 4, y - 3)
Triangle ABC will be converted to A'B'C' with A'(x1 + 4, y1 - 3), B'(x2 + 4, y2 - 3) and C'(x3 + 4, y3 -3)
If we calculate the distance between A and A' (AA') using the distance formula
AA' = sqrt( (x1+4-x1)^2 + (y1-3-y1)^2) = sqrt(16+9) = 5
The same distance is in between BB' and CC'