Asegment measures 10 units. one end of the segment has an endpoint at three, -6. what is another possible in point to this segment

Assumingn ya mean the oint (3,-6)

add or subtract 10 from x or y to get points 10 away

3-10=-7 so a point is (-7,-6)
3+10=13 so a point is (13,-6)
-6-10=-16 so a point is (3,-16)
-6+10=4 so a point is (3,4)

those are 4 out of inifnite points that we can get that are 10 units from (3,-6)
the points are (x,y) such that they satisfy the following equation:

Socrat use det app ok