Question

If A(2,-1)B(-1,3)andC(6,7) are the vertices of a triangle ABC ,then what is the length of median through vertex B

Answer 1

x=(x1+x2)/2
y=(y1+y2)/2
(mid pt. theo.)
x=(2+6)/2=4
y=(-1+7)/2=3
(x,y)=(4,3)
distance between B&(x,y)
=under root (4-(-1))square+(3-3)square
=under root25
=5(answer)

Answer 2

Answer:

5 units.

Step-by-step explanation:

Given information: A(2,-1), B(-1,3) and C(6,7).

Median through vertex B divides the side AC in two equal parts.

Let BD is a median, so D is the midpoint of AC.

$Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

$D=(\dfrac{2+6}{2},\dfrac{-1+7}{2})$

$D=(\dfrac{8}{2},\dfrac{6}{2})$

$D=(4,3)$

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Length of median through vertex B is

$BD=\sqrt{\left(4-\left(-1\right)\right)^2+\left(3-3\right)^2}$

$BD=5$

Therefore, the length of median through vertex B is 5 units.