If $D$, $E$ and $F$ are the middle points of $BC$, $CA$ and $AB$ respectively then the area of the triangle $DEF$ is:
Step-by-Step Solution
Key Concept: The ratio of areas of similar triangles equals the square of the ratio of corresponding sides; use coordinates to compute areas directly.
Given that area of $\triangle DEF = \frac{1}{4}$ area of $\triangle ABC$ with vertices $A(9, 3)$, $B(7, -1)$, $C(1, -1)$. The area of $\triangle ABC = \frac{1}{2} \times 6 \times 4 = 12$, so area of $\triangle DEF = 3$. Point $D$ lies on $AB$ and $E$ on $BC$ such that the triangle $DEF$ is formed with the specified area constraint.
Correct Answer: 4