Question

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

Answer 1

Answer:

Therefore area of a triangle whose vertices are (0,0), (4,2), (-1,2) is

5 units².

Step-by-step explanation:

Given:

Let the vertices be,

point A( x₁ , y₁) ≡ ( 0 , 0)

point B( x₂ , y₂) ≡ (4 , 2)

point C(x₃ , y₃ ) ≡ (-1 , 2)

To Find:

Area of Triangle = ?

Solution:

If the Vertices A( x₁ , y₁), B( x₂ , y₂) and C(x₃ , y₃ ) then the Area of Triangle is given by

$\textrm{Area of Triangle}=\dfrac{1}{2}(x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}))$

Substituting the values we get

$\textrm{Area of Triangle}=\dfrac{1}{2}(0(2-2)+4(2-0)+(-1)(0-2))$

$\textrm{Area of Triangle}=\dfrac{1}{2}(0+8+2))=\dfrac{10}{2}=5\ units^{2}$

Therefore area of a triangle whose vertices are (0,0), (4,2), (-1,2) is

5 units².