Question

What is the area of a triangle whose vertices are (a , b + c), (a, b - c) and (-a, c)?

• A. 2ab
• B. 4ac
• C. 2ac
• D. 4ab

Answer 1

The correct option is C

2ac

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

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

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

The area of a triangle can never be a negative quantity, therefore a modulus of the value is taken whenever the calculated value is negative. Hence the area is $2ac.$