Question

if the vertices of triangle ABC A(5,-1)B(-3,-2)C(-1,8).find the length of median throughA

Answer 1

first find D by midpoint formula then find distance or length of AD by distance formula. Answer is root65

Answer 2

Answer: √65 unit

Step-by-step explanation: Given: A(5,-1) B(-3,-2) C(-1,8)

Let AD is the median. So D is the midpoint of BC.

Hence, By mid point Formula which states that $(x,y)=(\dfrac{x_{1}+x_{2} }{2} ,\dfrac{y_{1}+y_{2} }{2})$

Now the coordinate of D is given by :

$(x,y)=(\dfrac{-3+(-1)}{2} ,\dfrac{-2+8 }{2})\\\\\Rightarrow(x,y)=(\dfrac{-4}{2} ,\dfrac{6 }{2})=(-2,3)$

Now the length of median AD is given by distance formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

So the length of AD is:

$\sqrt{(-2-5)^2+(3-(-1))^2} =\sqrt{(-7)^2+4^2} =\sqrt{49+16} =\sqrt{65}$

Thereefore, the length of median is √65 unit