The x - coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as 0 , 1 , 1 , 1 and 1 , 0 is

Step-by-step solution

Let x 1 ,   y 1 ,   x 2 ,   y 2 and x 3 ,   y 3 be the vertices of a triangle, So, x 1 + x 2 = 0 ,   x 2 + x 3 = 2 ,   x 3 + x 1 = 2 [mid point formula x 1 + x 2 2 ] Similarly, y 1 + y 2 = 2 ,   y 2 + y 3 = 2 ,   y 3 + y 1 = 0 So, the vertices are 0 ,0 ,   0 ,2 ,   2 , 0 . We know that x -coordinate of incentre x ¯ = a x 1 + b x 2 + c x 3 a + b + c a = 2 , b = 2 , c = 2 2 , x 1 = 0 , x 2 = 2 , x 3 = 0 ∴     x ¯ = 0 + 4 + 0 2 + 2 + 2 2 &#865