Question

Find the area of triangle whose vertices are (0,0) (-2,3) (10,7)

Answer 1

First take the coordinates point as A ;B ;and C

Answer 2

Answer:

Area of Triangle = 22 unit²

Step-by-step explanation:

Given: Coordinates of vertices of a triangle say ΔABC

           $A(x_1,y_1)=(0,0)\:,\:B(x_2,y_2)=(-2,3)\:and\:C(x_3,y_3)=(10,7)$

To find: Area of ΔABC

When Coordinates of vertices of a triangle is given then area of triangle is given by,

$Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$

using this formula we get,

$Area\,of\,triangle\,=\,\frac{1}{2}\left|0(3-7)+(-2)(7-0)+10(0-3)\right|$

                                   = $\frac{1}{2}\left|-2\times7+10\times(-3)\right|$

                                   = $\frac{1}{2}\left|-14-30\right|$

                                   = $\frac{1}{2}\left|-44\right|$

                                   = $\frac{1}{2}\times44$

                                   = 22 unit²

Therefore, Area of Triangle = 22 unit²