Question

The area of the triangle formed by the points

$(a,b + c),(b,c + a),(c,a + b)$ is

• A. abc
• B. $a^{2} + b^{2} + c^{2}$
• C. $ab + bc + ca$
• D. 0

Answer 1

Answer: (D)

0

Answer 2

Area = $\frac{1}{2}\left| \begin{matrix} a & b + c & 1 \\ b & c + a & 1 \\ c & a + b & 1 \end{matrix} \right|$=$\frac{1}{2}\left| \begin{matrix} a & a + b + c & 1 \\ b & b + c + a & 1 \\ c & c + a + b & 1 \end{matrix} \right|$,

(Applying $C_{2} \rightarrow C_{1} + C_{2}$) = $\frac{a + b + c}{2}\left| \begin{matrix} a & 1 & 1 \\ b & 1 & 1 \\ c & 1 & 1 \end{matrix} \right|$=0