find the area of triangle formed by mid point of the side of triangle are A=(1,2) B=(-2,3) and C=(-3-4)
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Step-by-step explanation:
mid point of AB=( ( 1-2)/2 , (3+2)/2 )
= ( -1/2,5/2) = (x1,y1) say
similarly mid point of BC.
= (-5/2,-1/2)= (x2,y2). say
mid point of CA= (-1,-1) = (x3,y3). say
area of triangle formed by mid points
= (1/2) [ (y1x2+y2x3+y3x1)
-(x1y2+x2y3+x3y1)]
(1/2) [ (-25/4+1/2+1/2) - ( 1/4+5/2-5/2)
= (1/2)[ -21/4 - 1/4]
=( 1/2) ×( -22/4)
= -22/8= -2 integer 3/4
but area is always positive.
=> area of required triangle
= 2 integer 3/4 unit²
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