Question

If A(5,-1), B(-3,-2) and C(-1,8) are the vertices of a triangle ABC, find the length of the median through A and the coordinates of the centroid.

Answer 1

Answer:

√65 unit ,. (1/3,5/3)

Step-by-step explanation:

let the mid point of BC be D

X- coordinate of mid point of BC = (-3-1)/2 = -2

Y- coordinate of mid point of BC = (-2+8)/2= 3

=> coordinate of mid point of BC = D: (-2,3)

=> length of the median passes through A

= length of line segment AD( median AD)

___________

=> AD = √ (5+2)²+(-1-3)²

_____

= √49+16

= √65 unit

the centroid divides AD in 2 : 1

=> X- coordinate of centroid

= ( 2×-2+1×5)/(2+1)

= (-4+5)/3 = 1/3

=> Y- coordinate of centroid

= (2×3+1×-1)/(2+1)

= (6-1)/3 = 5/3

=> coordinate of centroid = ( 1/3,5/3)

formula used

(1) coordinate of mid point of a line segment which coordinate of end points are (x1,y1) and (x2,y2)

= [(x1+x2)/2, (y1+y2)/2]

if a point lies on it and divides in the ratio

m : n, the coordinates will be

x = (mx2+nx1)/(m+n)

y = ( my2+ny1)/(m+n)

hope this helps you