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: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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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:

Solution & Step-by-step Explanation

1. Let the vertices be A (x_{1}, y_{1}), B (x_{2}, y_{2}), C (x_{3}, y_{3}) .Midpoints: \frac{A + B}{2} = (0, 1), \frac{B + C}{2} = (1, 1), \frac{C + A}{2} = (1, 0) .Solving: A (0, 0), B (0, 2), C (2, 0) .2. Side lengths: c = A B = 2, a = BC = (2 - 0)^{2} + (0 - 2)^{2} = 22, b = C A = 2 .3. x -coordinate of Incentre I = \frac{a x _{1} + b x _{2} + c x _{3}}{a + b + c} : x_{I} = \frac{2 2 ( 0 ) + 2 ( 0 ) + 2 ( 2 )}{2 2 + 2 + 2} = \frac{4}{4 + 2 2} = \frac{2}{2 + 2} Multiply by conjugate: \frac{2 ( 2 - 2 )}{4 - 2} = \frac{2 ( 2 - 2 )}{2} = 2 - 2 .

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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:

2 - \sqrt{2}

1 + \sqrt{2}

1 - \sqrt{2}

2 + \sqrt{2}

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