You have that the midpoint in between the points A and B is:
M(2,4)
Furthermore, you have that point A is A(-2,9).
In order to determine which are the coordinates of point B, you take into accoun the following formula for calculating the coordinates of the midpoint:
x = (x1 + x2)/2
y = (y1 + y2)/2
where x and y are the coordinates of the midpoint, and (x1,y1) and (x2,y2) are the coordinates of point A and B rspectively. That is, you have:
(x1,y1) = A(-2 , 9)
x = 2
y = 4
To find the values of x2 and y2, you replace the previous values of x, y, x1 and y1 into the expression for the midpoints, and then you solve for x2 and y2, just as follow:
x = (x1 + x2)/2 replace
2 = (-2 + x2)/2 multiply by 2 both sides
4 = -2 + x2 add 2 both sides
6 = x2
y = (y1 + y2)/2 replace
4 = (9 + y2)/2 multiply by 2 both sides
8 = 9 + y2 subtract 9 both sides
-1 = y2
Hence, you have that the coordinates of the point B are:
(6 , -1)