Question

In triangle MNO if mp is median show that MN`2+MO`2=2(Mp`2+NP`2)

Answer 1

Answer:

Step-by-step explanation:

Let M is zero vector .

Q is middle in NO  

so, Q is vector ( M + O)/2  

E is the middle point of MQ.

so, E is vector {M+ O }/4  

eqn of MO :  

r = (1 - s) 0 + sO _________(1)

where s is constant.

r = sO  

again, eqn of QE  

r = (1 -t) Q +t (M+ O)/4_____(2)

where t is constant  

solve eqns (1) and (2)  

t = 4/3 and s = 1/3  

hence, eqn of MO :  

r = 1/3 O________(3)

now, eqn of MO from section formula ,  

r = ß O /(ß + 1)______(4)

compare (3) and (4)  

ß /(ß + 1) = 1/3  

ß = 1/2  

hence,  

MR/MO = 1/3  

MR/30 = 1/3

MR = 10 cm