midpoint M is ( (-1+6)/2 , (-2+2)/2 ) = ( 5/2 , 0)
midpoint N is ( (-1+4)/2 , (-2+6)/2 ) = ( 3/2 , 2)
slope BC = (6-2)/(4-6) = 4/-2 = -2
slope of MN - (0-2)/(5/2 - 3/2) = -2
So BC is || to MN
length of BC = √( (6-2)^2 + (4-6)^2) = √(16+4)
= √20 = 2√5
length of MN = √( (0-2)^2 + (5/2-3/2)^2
= √( 4+1) = √5
which is 1/2 of BC
The points A(-1,-2) B(6,2) and C(4,6) form a triangle ABC. M is the mid-point of AB and N is the mid-point of AC.
Prove that MN is parallel to BC and equal in length to half the length of BC.
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