If the mid-points of the sides A B, B C, C A of a triangle are (1,5,-1),(0,4,-2),(2,3,4) respectively, then the length of the median drawn from C to A B is

Step-by-step solution

D(1,5,-1), E(0,4,-2), F(2,3,4) are mid-points Then, aligned & x₁+x₂ 2 =1 y₁+y₂ 2 =5 z₁+z₂ 2 =-1 & x₁+x₂=2, y₁+y₂=10, z₁+z₂=-2 aligned Similarly, array lll x₂+x₃=0, & y₂+y₃=8, & z₂+z₃=-4 x₁+x₃=4, & y₁+y₃=6, & z₁+z₃=8 array On adding, 2 (x₁+x₂+x₃ )=6 , aligned & 2 (y₁+y₂+y₃ )=24, 2 (z₁+z₂+z₃ )=2 & x₁+x₂+x₃=3, y₁+y₂+y₃=12 & z₁+z₂+z₃=1 & x₃=1, y₃=2, z₃=3 & aligned length of median drawn from C to A B is aligned C D & = (1-1)^2+(2-5)^2+(-1-3)^2 & = 0+9+16 = 25 =5 aligned