Let A (0,0), B(3,0), C(0,-4) are vertices of A B C then the co-ordinates of incentre of A B C is

Step-by-step solution

Given vertices A(0,0) , B(3,0) , and C(0,-4) , the side lengths are found using the distance formula. Side a opposite A is BC = (3-0)^2 + (0 - (-4))^2 = 9 + 16 = 5 . Side b opposite B is AC = (0-0)^2 + (-4-0)^2 = 4 . Side c opposite C is AB = (3-0)^2 + (0-0)^2 = 3 . The incenter coordinates are given by I = ( a x₁ + b x₂ + c x₃ a + b + c , a y₁ + b y₂ + c y₃ a + b + c ) . x = 5 0 + 4 3 + 3 0 5 + 4 + 3 = 12 12 = 1 y = 5 0 + 4 0 + 3 (-4) 12 = -12 12 = -1 The incenter is (1, -1) , matching option B .