Question

Find the area of the triangle whose vertices are (2,3), (-1,0), (2,-4) ?​

Answer 1

Go and do this sum u will get

Answer 2

Question :

Find the area of the triangle whose vertices are (2,3), (-1,0), (2,-4) ?

Formula :

The area of triangle having vertices $\tt ({x}_{1},{y}_{1}),({x}_{2},{y}_{2}) \:and\:({x}_{3},{y}_{3})$

A = $\left| \begin{array}{c c c} {x}_{1}& {y}_{1}&1 \\ {x}_{2} & {y}_{2} & 1 \\ {x}_{3} & {y}_{3} & 1 \right| \end{array}$

Solution :

A = $\left | \begin{array}{ccc} 2& 3&1 \\ - 1& 0 & 1 \\ 2 & -4 & 1 \right | \end{array}$

$\tt \implies$ A = $\tt \frac{1}{2}$ 2(1×0 - 1×-4) - 3( -1×1 - 2×1) + 1(-4×-1 - 2×0)

$\tt \implies$ A = $\tt \frac{1}{2}$ 2(0+4) -3(-1-2) + 1(4-0)

$\tt \implies$ A = $\tt \frac{1}{2}$ 2×4 -3×-3 + 1×4

$\tt \implies$ A = $\tt \frac{1}{2}$ 8 + 9 + 4

$\tt \implies$ A = $\tt \frac{1}{2}$ 21

$\tt \implies$ A = $\tt \frac{21}{2}$

Area of triangle is 21/2 sq.units.