Discussion Forum

  The x- coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as (0,1),(1,1) and (1,0) is

Answer:

Explanation:

 Given midpoints  of a triangle are (0,1),(1,1)  and (1,0) . Plotting these points on graph paper and make a triangle. 

 So the sides of a triangle will be 2,2 and  $\sqrt{2^{2}+2^{2}}$  $i.e 2\sqrt{2}$

 x- coordinate of incentre

  =$\frac{2\times0+2\sqrt{2}.0+2.2}{2+2+2\sqrt{2}}$

  $=\frac{2}{2+\sqrt{2}}\times\frac{2-\sqrt{2}}{2-\sqrt{2}}=2-\sqrt{2}$