Answer:
(-1.92, 1.08)
Explanation:
The incenter is the center of the largest circle that can be inscribed in the triangle. That circle is called the incircle. The incenter is at the point of intersection of the angle bisectors. For a right triangle, the inradius (the radius of the incircle), is found from a simple formula:
r = (a + b - c)/2 . . . . . where c is the hypotenuse, and a and b are the legs
In your triangle, the inradius is ...
r = (5 + 3 -√(5² +3²))/2 = 4 -√8.5 ≈ 1.08452
Among other things, this means the coordinates of the incenter are about (1.08, 1.08) from the right angle vertex, so are about ...
incenter ≈ (-1.92, 1.08)