Question

If ( - 4, 6) , (2,3) and (-2,-5) are the vertex of triangle then its incentre is

Answer 1

Answer

Incentre (x,y)= (-1,2)

Solution

If A( - 4, 6) , B(2,3) and C(-2,-5) are the vertex of triangle then its Incentre is

(x,y)= [(ax₁ + bx₂ + cx₃)/(a+b+c),(ay₁ + by₂ + cy₃)/(a+b+c)]

a= BC =  4$\sqrt{5}$ (Using distance formula)

b = AC = 5$\sqrt{5}$ (Using distance formula)

c = AB = 3$\sqrt{5}$ (Using distance formula)

a+b+c=12$\sqrt{5}$

Incentre of triangle ABC (x,y) =$\frac{-16\sqrt{5}+10\sqrt{5}-6√5}{12\sqrt{5}}$  , $\frac{24\sqrt{5} + 15\sqrt{5} -15\sqrt{5}}{12\sqrt{5}}$

       (x,y)= (-1,2)