Question

Three points A, B and C have coordinates $(a,b+c),(b,c+a)$ and $(c,a+b)$, respectively. The area of the triangle ABC will be:

• A. $a^2+b^2+c^2$
• B. $\frac{a^2+b^2+c^2}{2}$
• C. $\frac{a^2+b^2+c^2}{4}$
• D. $0$

Answer 1

The correct option is D $0$

Area of triangle $=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

Given the points: $A(a,b+c),B(b,c+a),C(c,a+b)$

Therefore, area:

$A=\frac{1}{2}\left[a\right(c+a-a-b)+b(a+b-b-c)+c(b+c-c-a\left)\right]$

$A=\frac{1}{2}\left[a\right(c-b)+b(a-c)+c(b-a\left)\right]$

$A=\frac{1}{2}[ac-ab+ba-bc+cb-ac]=0$