The incenter of the triangle formed by the points (0,0,0),(3,0,0) and (0,4,0) is

Step-by-step solution

Let A(0,0,0), B(3,0,0), C(0,4,0) Now, aligned & a= (0-3)^2+(4-0)^2+(0-0)^2 =B C & a= 25 =5 aligned and b=A C= 0+4^2+0 =4 and c=A B= 3^2+0+0 =3 Now, coordinate of incentre (x, y, z) is given as x= a x₁+b x₂+c x₃ a+b+c aligned & = 15(0)+(4)(3)+(3)(0) 5+4+3 =1 y & = a y₁+b y₂+c y₃ a+b+c = (5)(0)+(4)(0)+(3)(4) 5+4+3 =1 z & = a z₁+b z₂+c z₃ a+b+c & = (5)(0)+(4)(0)+(3)(0) 5+4+3 =0 (x, y, z) & =(1,1,0) aligned