Question

The virtice of a triangle abc are a -3,2 b -1,-4 and c 5,2 . If m and n are the mid points of ab and ac respectively, show that 2mn =BC

Answer 1

Answer:

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Answer 2

Given : The virtice of a triangle abc are a -3,2 b -1,-4 and c 5,2  m and n are the mid points of ab and ac respectively,

To Find : Show that 2mn = BC

Solution:

A ( - 3, 2)

B (- 1 , - 4)

C = ( 5 , 2)

BC = √( (5 - (-1))²  + (2 - (-4))² )

=> BC = √ ( 6² + 6²)

=> BC = 6√(1 + 1)

=> BC = 6 √2

m is mid point of AB  ,  A ( - 3, 2)    , B (- 1 , - 4)

m = ( (-3 - 1)/2  , (2 - 4)/2)

=> m = ( -2 , - 1)

n is mid point of AC  ,  A ( - 3, 2)    , C (5, 2)

n = ( (-3+5)/2  , (2 + 2)/2)

=> n = ( 1 , 2)

m = ( -2 , - 1)   ,  n = ( 1 , 2)

=> mn =  √( (1 - (-2))²  + (2 - (-1))² )

=> mn = √ ( 3² + 3²)

=> mn =  3√(1 + 1)

=> mn = 3√2

=> 2mn = 2 *  3√2

=> 2mn = 6√2

=> 2mn = BC

QED

Proved

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