Question

Find the area of the triangle formed by joining the mid-points of the sides whose vertices are (0, -1), (2, 1) and (0, 3). Also find the ratio of the given triangle to the newly formed triangle.

Answer 1

$A(0,-1),B(2,1)$ and $C(0,3)$

Mid-points of AB,BC&CD=>$D(1,0),E(1,2)$ and $F(0,1)$

Area of $△DEF=\frac{1}{2}\left|\begin{array}{cc}1& 0\\ 1& 2\\ 0& 1\\ 1& 0\end{array}\right|=\frac{1}{2}|2+1-1|=1sq.units$

Area of $△ABC=\frac{1}{2}\left|\begin{array}{cc}0& -1\\ 2& 1\\ 0& 3\\ 0& -1\end{array}\right|=4sq.units$

$\frac{Areaof△DEF}{Areaof△ABC}=\frac{1}{4}$