Question

Question 7
The area of a triangle with vertices A(3,0), B(7,0) and C(8,4) is
(A) 14
(B) 28
(C) 8
(D) 6

Answer 1

Area of $\Delta ABC$ whose vertices are $A(x_1,y_1),B(x_2,y_2)$ and $C(x_3,y_3)$ are given by
$\left|\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]\right|Here,x_1=3,y_1=0,x_2=7,y_2=0,x_3=8and{y}_3=4\therefore \Delta =\left|\frac{1}{2}\left[3\right(0-4)+7(4-0)+8(0-0\left)\right]\right|$
$=\left|\frac{1}{2}(-12+28+0)\right|=\left|\frac{1}{2}\right(16\left)\right|=8$