Question

3. 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
​

Answer 1

Answer:

since D,E and F are the midpoints of AB, BC and CA of triangle respectively

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