Question

Area of the triangle with vertices P(5, 2), Q(-9, -3) and R(-3, -5) (in sq units) is

• A. $58$
• B. $14$
• C. $29$
• D. None

Answer 1

The correct option is C $29$

Area of a triangle with vertices $(x_1,y_1)$ ; $(x_2,y_2)$ and $(x_3,y_3)$ is $\left|\frac{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}{2}\right|$
Hence, substituting the points $(x_1,y_1)=(5,2)$ ;
$(x_2,y_2)=(-9,-3)$ and $(x_3,y_3)=(-3,-5)$ in
the area formula, we get area $=\left|\frac{5(-3+5)+(-9)(-5-2)+(-3)(2+3)}{2}\right|=\left|\frac{10+63-15}{2}\right|=\left|\frac{58}{2}\right|=29squnits$