Question

In $△ABC$, the coordinates of vertex A are (0, -1) and D (1, 0) and E (0, 1) respectively the mid-pointd of the sides AB and AC. If F is the mid -point of side BC, Find the area of $△DEF$.

Answer 1

The lines joining midpoints of sides of triangle divides the triangle in small 4 triangles of equal areas.
Ar ADE = Ar BDF =Ar FEC = Ar DFE = Ar ABC

Ar DFE = Ar ADE = |(0-(-1)+(1-0)+0|) = 1 sq unit