Question

angle formed by joining the midpoints of the sides of the triangle whose vertices are (0,-1) (2,1) (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

Explanation:

Answer 2

Answer:

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