The vertices of a triangle are (2, 1), (-2, 3) and
(4, -3). Find the area of the triangle received
by joining the midpoints of the sides of
this triangle.
Answers
Answered by
2
Answer:
coordinate of D=(
2
0+2
,
2
−1+1
)=(1,0)
coordinate of E=(
2
2+0
,
2
1+3
)=(1,2)
coordinate of F=(
2
0+0
,
2
−1+3
)=(0,1)
∴ar(△DEF)=
2
1
[1(2−1)+1(1−0)+0(0−2)]=1sq.unit
andar(△ABC)=
2
1
[0(1−3)+2(3+1)+0(−1−1)]=4sq.unit
ar(△ABC)
ar(△DEF)
=
4
1
⇒ar(△DEF):ar(△ABC)=1:4
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