Question

The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.

• A. 0
• B. 1
• C. a + b + c
• D. $a^2$ + $b^2$ + $c^2$

Answer 1

The correct option is A

0

Area of a triangle with vertices $(x_1,y_1),(x_2,y_2)and(x_3,y_3)$ is given by
$Area=\frac{1}{2}\times |\left(x_1\right)(y_2-y_3)+\left(x_2\right)(y_3-y_1)+\left(x_3\right)(y_1-y_2)|$

Thus, $\text{Area of the given triangle}$
$=\frac{1}{2}|a(c+a-a-b)+b(a+b-b-c)+c(b+c-c-a)|$
$=\frac{1}{2}|ac-ab+ab-bc+bc-ac|=0$