The rule of the midpoint (x, y) of a line that has two endpoints (x1, y1) and (x2, y2) is
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ y=\frac{y_1+y_2}{2} \end{gathered}[/tex]Since CD is bisected by B, then
B is the midpoint of CD
Then B = (x, y)
Since B = (8, 14), then
x = 8 and y = 14
Since C = (-9, -1), then
x1 = -9 and y1 = -1
We will use the rule of the midpoint above to find (x2, y2) the coordinates of point D
[tex]8=\frac{-9+x_2}{2}[/tex]Multiply both sides by 2
[tex]16=-9+x_2[/tex]Add 9 to both sides
[tex]\begin{gathered} 16+9=-9+9+x_2 \\ 25=x_2 \end{gathered}[/tex]The x-coordinate of point D is 25
[tex]14=\frac{-1+y_2}{2}[/tex]Multiply both sides by 2
[tex]28=-1+y_2[/tex]Add 1 to both sides
[tex]\begin{gathered} 28+1=-1+1+y_2 \\ 29=y_2 \end{gathered}[/tex]The y-coordinate of point D is 29, then
Point D = (25, 29)
We used the equation of the mid-point
[tex]\begin{gathered} x_D=2(x)-x_c \\ y_D=2(y)-y_c \end{gathered}[/tex]