question_answer

If \[A(2,2),\,B(4,4)\] and \[C(2,6)\] are the vertices of a triangle ABC and D, E and F are the mid point of AB, BC and AC respectively, then

(i)   Find the area of MBC.

(ii)  Find the area of ADEF.

(iii) Find the ratio of area of ADEF to MSQ

           

A)

(i)	(ii)	(iii)
8 sq. units	2 sq. units	\[1:4\]

               

B)

(i)	(ii)	(iii)
6 sq. units	3 sq. units	\[1:2\]

               

C)

(i)	(ii)	(iii)
4 sq. units	1 sq. units	\[1:4\]

               

D)

(i)	(ii)	(iii)
3 sq. units	1 sq. units	\[1:3\]

Correct Answer: C

Solution :

Given \[A(2,2),\]\[b(4,4),\]AND \[C(2,6)\] are the vertices of \[\Delta ABC\], D, E and F are mid points of AB, BC and AC respectively. (i) Area of \[\Delta ABC\] \[=\frac{1}{2}\left| [2(4-6)+4(6-2)+2(2-4)] \right.\] \[=\frac{1}{2}\left. \left| [2(-2)+4(4)+2(-2)] \right. \right|=4\,sq.\]units (ii) Area of \[\Delta DEF=\frac{1}{4}\] (Area of \[\Delta ABC\]) \[=\frac{1}{4}(4)=1sq.\,\]units (iii) Required ratio \[=\frac{1}{4}=1:4\]