Question

find the area of triangle abc whose vertices are a(2,2) b(3,4) and c(-1,3)​

Answer 1

area of triangle abc whose vertices are a(2,2) b(3,4) and c(-1,3)

Answer 2

Area of triangle with vertices (2,2), (3,4), (-1,3) is $\frac{7}{2}$

Step-by-step explanation:

Given vertices of triangle are a(2,2) , b (3,4), c(-1,3)

=> Assuming the given points as :

(x₁ , y₁) = (2,2)

(x₂ , y₂) = (3,4)

(x₃ , y₃) = (-1,3)

=> We know that the area of triangle whose vertices are given can be calculated as:

$Area = \frac{1}{2} (x_{1}(y_{2} - y_{3}) + x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2}))\\\\Substituting \ the \ values \ of \ x_{1} ,x_{2},x_{3},y_{1},y_{2},y_{3}\\\\ Area = \frac{1}{2} (2(4-3) + 3(3-2)-1(2-4))\\\\ Area = \frac{1}{2}(2(1)+ 3(1)-1(-2))\\\\Area = \frac{1}{2}(2+3+2)\\\\Area = \frac{1}{2}(7)\\\\Area = \frac{7}{2}$

=> The area of given triangle is $\frac{7}{2}$