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Question

Mathematics Question on Straight lines

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

A

2+22+\sqrt{2}

B

2−22-\sqrt{2}

C

1+21+\sqrt{2}

D

1−21-\sqrt{2}

Answer

2−22-\sqrt{2}

Explanation

Solution

Given m id-points of a triangle are (0, 1), (1, 1) and (1, 0). P lotting these points on a graph paper and make a triangle.
So, the sides of a triangle will be 2, 2 and22+22i.e.22\sqrt{2^2+2^2} i.e. 2\sqrt{2}
x-coordinate of incentre=2×0+22.0+2.22+2+2=\frac{2\times0+2\sqrt{2}.0+2.2}{2+2+\sqrt{2}}
=22+2×2−22−2=2−2=\frac{2}{2+\sqrt{2}}\times\frac{2-\sqrt{2}}{2-\sqrt{2}}=2-\sqrt{2}