Question

Area of triangle formed by the points (-2,0) (0,-2) and (2,0) is

Answer 1

$\text{Concept:}$

$\text{Area of the triangle formed by the points }(x_1, y_1),\,(x_2, y_2)\text{ and }(x_3, y_3)\text{ is}$

$\boxed{\bf\triangle=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]}$

$\text{Given points are (-2,0), (0,-2) and (2,0) }$

$\text{Area of the triangle formed by the points (-2,0), (0,-2) and (2,0)}$

$\triangle=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

$\implies\triangle=\frac{1}{2}[(-2)(-2-0)+(0)(0-0)+2(0+2)]$

$\implies\triangle=\frac{1}{2}[4+0+4]$

$\implies\triangle=\frac{1}{2}[8]$

$\implies\triangle=4\text{ square units}$

Find more:

If the points (2a,a),(a,2a) and (a,a) enclose a triangle of area 18 square units. Then the centroid of the triangle is:

https://brainly.in/question/9522665

Answer 2

Given: Three points are $(-2,0) (0,-2)\ and\ (2,0)$

To Find: Area of the Triangle.

Step-by-step explanation:

We have the formula to find the Area of triangle when given three points,

$\triangle=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$__1

Where,

$x_{1}=-2\\y_{1}=0\\x_{2}=0\\y_{2}=-2\\x_{3}=2\\y_{3}=0$

Plug all the value in equation-1,

$\triangle=\frac{1}{2}[-2(-2-0)+0(0-0)+2(0-(-2))]$

⇒$\triangle=\frac{1}{2}[4+0+4]$

⇒$\triangle=\frac{1}{2}[8]$

⇒$\triangle=4$ square units

So, The Area of Triangle is $4$ square units.