M is the midpoint of line AB . If A is at ( 5,7) and M is at ( -3,-4). find the coordinates of B.?

Let (x, y) be the coordinates of B.

(x + 5)/2 = -3
x + 5 = -6
x = -11

(y + 7)/2 = -4
y + 7 = -8
y = -15

The coordinates of B = (-11, -15)

M is the midpoint / average / arithmetic mean of A and B.
(A+B)/2 = M, so B = 2M-A
B = (2*-3-5, 2*-4-7) = (-11, -15)

The coordinates of B is (-11, -15)

B ( -11 , -15 )

Recall: midpoint of A (x1,y1) and B (x2,y2) is
[(x1+x2)/2, (y1+y2)/2].

This implies that:

(5+x2)/2 = -3 and (7+y2)/2 = -4

Solving, we get x2 = -11 and y2 = -15.

Therefore coordinates of B is (-11,-15).