Please help with this math problem.

Question

Point B has coordinates (5​,2​). The​ x-coordinate of point A is negative −4. The distance between point A and point B is 15 units. What are the possible coordinates of point​ A?

Answer 1

Since point A lies on the line x=-4, a line drawn perpendicular to it that passes thru (5,2) would intersect at (-4,2). That segment would be 5-(-4)=9 units long. Since we know the segment connecting A to B is 15 long and that makes up the hypotenuse of the 2 possible right triangles that were formed, we can use the Pythagorean Theorem to determine the two possibilities for point A.

a²+b²=c² -> a²+9²=15² -> a²=225-81=144 -> a=+/- 12

So point A is either at (-4,14) or (-4,-10)