Triangle abc has vertices a(1,5) b(9,7) and c(7,13) m is the midpoint of ab and n is the midpoint of bc. which of the following is the length of mn? a.3 b.4 c.5 d.6

By Mid Point Formula ,

In the cordinates of Mid point ,



Applying formula for pt. M

Cordinates of A = ( 1 , 5 )
Cordinates of B = ( 9 , 7 )

So,





So, M = ( 5 , 6 )

Now applying formula for pt. N

Cordinates of B = ( 9 , 7 )
Cordinates of C = ( 7 , 13 )

So,





N = ( 8 , 10 )

Now ,

By Distance formula ,

M = ( 5 , 6 )



N = ( 8 , 10 )



Therefore,






Distance = √25

Distance = 5 units