Question

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. Question from Class 10 Chapter Coordinate Geometry

Answer 1

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