Answer: The length of the median from angle B is 8 units.
Step-by-step explanation: As shown in the attached figure, A(-6, 7), B(4, -1) and C(-2, -9) are the vertices of ΔABC.
We are to find the length of the median BD from angle B to side AC.
Since BD is the median on side AC. So, D will be the mid-point of side AC.
Therefore, the co-ordinates of the point 'D' are
[tex]\left(\dfrac{-6+(-2)}{2},\dfrac{7+(-9)}{2}\right)=\left(\dfrac{-8}{2},\dfrac{-2}{2}\right)=(-4,-1).[/tex]
Now, the length of median BD is equal to the distance between the vertex 'B' and the point 'D'.
Therefore, the length of median BD calculated using distance formula is
[tex]BD=\sqrt{(-4-4)^2+(-1+1)^2}\\\\\Rightarrow BD=\sqrt{64+0}\\\\\Rightarrow BD=\sqrt{64}\\\\\Rightarrow BD=8.[/tex]
Thus, the length of the median from angle B is 8 units.
