Point b has coordinates ​(1​,2​). the​ x-coordinate of point a is negative −11. the distance between point a and point b is 15 units. what are the possible coordinates of point​ a?

The distance between points is given by the following equation:
 d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)
 Substituting we have:
 15 = root ((- 11-1) ^ 2 + (a-2) ^ 2)
 We clear the value of a:
 (15) ^ 2 = (root ((- 11-1) ^ 2 + (a-2) ^ 2)) ^ 2
 225 = (- 11-1) ^ 2 + (a-2) ^ 2)
 Rewriting:
 225 = 144 + (a-2) ^ 2
 225-144 = (a-2) ^ 2
 81 = (a-2) ^ 2
 a-2 = +/- root (81)
 a = +/- 9 + 2
 The possible values are:
 a1 = 9 + 2 = 11
 a2 = -9 + 2 = -7
 Then, the possible coordinates of point a are:
 (-11, 11)
 (-11, -7)
 Answer:
 the possible coordinates of point a are:
 (-11, 11)
 (-11, -7)