Asked by Reema
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.
Prove that MN is parallel to BC and equal in length to half the length of BC.
Answers
Answered by
Reiny
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
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
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