Question

A village do notes his land to panchayat for village hospital which is in the shape of parallelogram. the three vertical of his land are (3,-4),(-1,-3) and ,find the coordinates of fourth vertex and find the area of land.​

Answer 1

Answer:

Let ABCD be the quadrilateral plot produced BA to meet DE draw parallel to EA at E to join EC

The △BAC and △ADC lie on the same parallel DE and CA

ar(EAC)−ar(ADC)

Now Ar(ABCD)=ar(ABC)+ar(ACD)

ar(ABC)+ar(EAC)=ar(EBC)

Ar(ABCD)=ar(ABC)+Ar(ADC)=ar(EBC)

∴ AR(ABCD)=Ar(EBC)