Question

find area of traingle whose vertices are (1,-1)(-4,6) and (3,-5).

Answer 1

If a triangle has three vertices namely (x₁,y₁),(x₂,y₂) and (x₃,y₃) then the area of that triangle will be :
Δ=(1/2)|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
=(1/2|1{6-(-5)}+(-4){-5-(-1)}+3(-1-6)|
=(1/2)|11+24-21|
=(1/2)|14|
=7 square unit

Answer 2

Area of triangle with vertices $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ is

$\frac{1}{2}|x_{1}(y_{2}-y_{3}) + x_{2}(y_{3}-y_{1}) + x_{3}(y_{1}-y_{2})|$

$\frac{1}{2}|1(6+5) + (-4)((-5)-1) + 3(-1-6)|$

$\frac{1}{2}|1(11) + (-4)(-6) + 3(-7)|$

$\frac{1}{2}|11 + 24 - 21)|$

7 sq units