L,M and N are the midpoints of the sides BC,CA and AB respectively of triangle ABC. If the vertices are A(3,−4),B(5,−2) and C(1,3) the area of △LMN is ____ square units.
2.75
2.5
2.25
3
A
2.25
B
2.5
C
3
D
2.75
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Solution
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The correct option is A 2.25
Area of triangle having vertices (x1,y1),(x2,y2) and (x3,y3) is given by =12×[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]
Let (x1,y1)=(3,−4), (x2,y2)=(5,−2) and (x3,y3)=(1,3)
Area of ΔABC=12[3(−2−3)+5(3+4)+1(−4+2)]
=12(−15+35−2)
=9 ∴ Area of ΔLMN=14×9=2.25 square units.
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