Question

The area of the triangle whose vertices are $A(1,1),B(7,3)$ and $C(12,2)$ is

• A. $25$ square units
• B. $8$ square units
• C. $16$ square units
• D. $12$ square units

Answer 1

Answer: (B)

$8$ square units

We know that the area of the triangle whose vertices are $(x_1,y_1),(x_2,y_2),$ and $(x_3,y_3)$ is $\frac{1}{2}\left|x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right|$

$\therefore$

Area $=\frac{1}{2}\left[1\right(1)+7(1)+12(-2\left)\right]=-8$, but area can not be negative

Hence, area = 8 square units.