Question

Find the mid-point of the sides of the triangle whose vertices are (0,-1),(2,1) and (0,3). hence find the length of each of its median

Answer 1

let A 〈 0, - 1 〉 B 〈 2 , 1 〉 C 〈 0 , 3 〉 vertices of ΔABC

Mid point of AB, L Ξ [ ( 0 + 2 ) / 2 , (-1 + 1) /2 ]

L Ξ ( 1 , 0 )

mid point BC , M Ξ [ ( 2+ 0 ) / 2 , ( 1+ 3 ) /2 ]

M Ξ ( 1 , 2 )

Mid point of CA , N Ξ [ (0+0) /2 , (-1 + 3 ) /2 ]

N Ξ ( 0 , 1 )

Now Medians are CL, BN, AM

A ( 0, -1) M(1, 2)

AM = √ ( 1-0)² + (-1 -2) ² = √ 10

CL = √ 10
BN = √ 4 = 2

Answer 2

See the attached file