The image point of A after a translation left 1 unit and down 2 units is the point B (1,-4). Determine the coordinates of the pre-image point A.

This is impossible to answer without the graph from the if you post the graph then we can .

Use pythagorean’s theorem and find the missing side lengths of the two smaller triangles and add them together
13^2 - 12^2 = 5
15^2 - 12^2 = 9
5+9 = 14
14 is the length of each side of the square
14^2 + 14^2 = 19.8
19.8 is the diagonal length of the inside if the square