Line segment AC is part of a line. Use the two-point formula to find the equation of the line:

(y-2) = ( (8-2)/(14-2) ) (x-2)

** y = (1/2)x + 1 [note: slope = 1/2]**

AC is **perpendicular** to the line of segment BD. The line containing segment BD has a slope of (-2), the negative reciprocal of (1/2). Use the point-slope formula to determine the equation of that line:

(y-4) = (-2)(x-11)

** y = -2x + 26 [equation of line with segment BD]**

To find the intersection point of line segment BD and AC. This is the **midpoint M** of segment BD.

(1/2)x + 1 = -2x + 26

x + 2 = -4x + 52

5x = 50

** x = 10**

then, use either equation to find y

y = (1/2)(10) + 1

** y = 6**

The line segments intersect at point M(10.6). This is the **midpoint** ("bisector") of segment BD.

Let the coordinates of D be (a,b) and use the midpoint formula:

10 = (11+a) / 2

20 = 11 + a

** a = 9**

6 = (4+b) / 2

12 = 4 + b

** b = 8**

**Point D is (9,8).**