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

Solution :

Given mid-points of a triangle are (0,1), (1,1) and (1,0).

So, by distance formula sides of the triangle are 2, 2 and \(2\sqrt{2}\).

x-coordinate of the incenter = \(2*0 + 2\sqrt{2}*0 + 2*2\over {2 + 2 + 2\sqrt{2}}\)

= \(2\over {2+\sqrt{2}}\)

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