Question

If $\Delta$ denotes the area of the triangle with vertices $(0,0),(5,0)$ and $(\frac{5}{6},\frac{25}{6}),$ then $\Delta$ is equal to

Answer 1

Area of a triangle by formula,
$\Delta =\left|\frac{a_x(b_y-c_y)+b_x(c_y-a_y)+c_x(a_y-b_y)}{2}\right|$
where $a_x$ and $a_y$ are the $x$ and $y$ coordinates of point $a$.

now using determinant formula of area of triangle we can say that

$12\Delta =12\left|\frac{0+\frac{125}{6}+0}{2}\right|$
$\Rightarrow 12\Delta =12\times \frac{125}{12}=125$