Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
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Since D,E and F are the midpoints of AB, BC and CA of triangle respectively
Coordinate of D=(20+2,2−1+1)=(1,0)
Coordinate of E=(22+0,21+3)=(1,2)
Coordinate of F=(20+0,2−1+3)=(0,1)
∴ar(△DEF) = 21
[1(2−1)+1(1−0)+0(0−2)]=1sq.unitandar(△ABC)=21
[0(1−3)+2(3+1)+0(−1−1)]=4sq.unitar(△ABC) ar (△DEF)
=41⇒ar (△DEF) :ar (△ABC)= 1 : 4
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Step-by-step explanation:
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Since D,E and F are the midpoints of AB, BC and CA of triangle respectively
Coordinate of D=(20+2,2−1+1)=(1,0)
Coordinate of E=(22+0,21+3)=(1,2)
Coordinate of F=(20+0,2−1+3)=(0,1)
∴ar(△DEF) = 21
[1(2−1)+1(1−0)+0(0−2)]=1sq.unitandar(△ABC)=21
[0(1−3)+2(3+1)+0(−1−1)]=4sq.unitar(△ABC) ar
(△DEF)
=41⇒ar (△DEF) :ar (△ABC)= 1 : 4