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 :

Engineering

Mathematics

Section Formulae and Centres of a Triangle

Question

$2 - \sqrt{2}$

$2 + \sqrt{2}$

$1 + \sqrt{2}$

$1 - \sqrt{2}$

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From using section formula three vertices are obtained as shown in figure.

Now, $x = \frac{{ax}_{1} + {bx}_{2} + {cx}_{3}}{a + b + c} = \frac{2 \sqrt{2} \times 0 + 2 \times 0 + 2 \times 2}{2 + 2 + 2 \sqrt{2}} = \frac{2}{2 + \sqrt{2}} = 2 - \sqrt{2}$