find the length of the median through the vertex b of a triangle abc w

1.	find the length of the median through the vertex b of a triangle abc with vertices A(9,-2),B(-3,7) and C(-1,10)
Answer» Given: A triangle ABC with vertices A(9,-2),B(-3,7) and C(-1,10) To find: The length of the median through vertex B. Solution: We KNOW that the median of any of the triangle is the mid-point of the sides of the triangle so, D is the mid-point of the AC Let the coordinate of point D is (x,y) Point D is given by: $(x,y) = \frac{x1+x2}{2} , \frac{y1+y2}{2}$ $(x,y) = \frac{9-1}{2} , \frac{-2+10}{2}$ $(x,y) = \frac{8}{2} , \frac{8}{2}$ $(x,y) = (4,4)$ Now we will find the length of the median BD by the distance formula, $\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$ $\sqrt{(9-4)^{2}+(-2-4)^{2}}$ $\sqrt{(5)^{2}+(-6)^{2}}$ $\sqrt{25+36}$ $\sqrt{61}$ The length of the median through vertex B is $\sqrt{61}$ UNITS