Question

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

Answer 1

Vertices of $△ABC$,$A(0,-1),B(2,1)$ and $C(0,3)$

Area of $△ABC$ $=\frac{1}{2}\left|\begin{array}{cc}0& -1\\ 2& 1\\ 0& 3\\ 0& -1\end{array}\right|=\frac{1}{2}\left|8\right|=4$

Mid-points AB,BC,CA be O,E,F respectively.

$D(1,0),E(1,2),F(0,1)$

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

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