Question

`A(6, 1), B(8, 2) and C(9, 4)` are three vertices of parallelogram ABCD. If E is the mid-point of DC, then find the area of `DeltaADE`.

Answer 1

Let the co-ordinates of point D be `(x_(4), y_(4))`
Now, the mid-point of BD = mid-point of AC
`rArr" "((x_(4)+8)/(2), (y_(4)+2)/(2))=((6+9)/(2), (1+4)/(2))`

`rArr" "(x_(4)+8)/(2)=(15)/(2)rArr" "x_(4)=7`
and `" "(y_(4)+2)/(2)=(5)/(2)" "rArr" "y_(4)=3`
`therefore" "D-= (7, 3)`
Mid-point E of CD `-=((7+9)/(2), (3+4)/(2))-=(8, (7)/(2))`
Now, area of `DeltaADE=(1)/(2)[6(3-(7)/(2))+7((7)/(2)-1)+8(1-3)]=(1)/(2)(-3+(35)/(2)-16)=-(3)/(4)`
`therefore` Area of `DeltaADE=(3)/(4)` square units (neglecting negative sign)