Question

If the vertices of abc are a(5,-11) b(-3,-2) and c(-1,8) find the length of median through triangle

Answer 1

x1,y1) = (5,-1) ….. (x2,y2) = (-3,-2) …. (x3,y3) = (-1,8) ……

So, centroid(X,Y) = { (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3 }

------->  (X,Y) = { (5 – 3 - 1 / 3) , (- 1- 2 + 8)/3) ……

------->  (X,Y) = (1/3 , 5/3) .......

For Median :):):):

let the point where median intersects the base be D(x,y) ......

As, the median bisects the base .....

(x,y) = { (x2  +  x3 )/2 , (y2 + y3)/2 }

------> (x,y) = { (-3-1)/2 , (-2+8)/2 }

------> (x,y) = (-2 , 3)

Now , the length of median is AD =   √(x - x1)2 +  (y - y1)2 

------>  AD = √(-2 - 5)2 +  (3 + 1)2

------>  AD = √(49 + 16)

------> AD = √65 units .......