Question

prove that the area formed by mid points of a side of a triangle is 1/4th of the area formed by its vertices​

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

Answer 2

Answer:

He stayed in a small room which was built on the dirty street. He used to sleep the whole day to avoid the expense of morning tea and meals of the afternoon. He would wake up at four in the evening every day. This was his whole day routine in the city.