Question

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

• A. $2+\sqrt{2}$
• B. $2-\sqrt{2}$
• C. $1+\sqrt{2}$
• D. $1-\sqrt{2}$

Answer 1

The correct option is B $2-\sqrt{2}$

Given mid-points of a triangle are (0, 1), (1, 1) and (1, 0). Plot these points on a graph paper and make a triangle.
So, the sides of a triangle will be 2, 2 and $\sqrt{2^2+2^2}$ i.e. $2\sqrt{2}$.

$x-coordinateofincentre=\frac{2\times 0+2\sqrt{2}.0+2.2}{2+2+2\sqrt{2}}\left(generalformulaforincentre\right)$
$=\frac{2}{2+\sqrt{2}}\times \frac{2-\sqrt{2}}{2-\sqrt{2}}=2-\sqrt{2}$