Question

5. Find the incentre of the triangle formed by the lines x= 1, y=1 and x + y = 1.​

Answer 1

Answer:

(square.root of 1/2,square root of 1/2)

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Answer 2

The incentre of the triangle formed by the lines x= 1, y=1 and x + y = 1 is given by,

Consider the attached figure, while going through the following steps.

Incenter of the triangle is given by the formula,

$I = (\dfrac{ax_1+bx_2+cx_3}{a+b+c}, \dfrac{ay_1+by_2+cy_3}{a+b+c})$

The given lines, x = 1, y = 1 and x + y = 1 intersect each other at points A (1, 1), B (0, 1) and C (1, 0).

we, have,

a = BC = √2

b = AC = 1

c = AB = 1

Therefore, the incenter is given by,

$I = (\dfrac{\sqrt 2 (1) +1(0) + 1 (1)}{\sqrt 2 +1+1}, \dfrac{\sqrt 2 (1) +1 (1) + 1 (0)}{\sqrt 2 +1+1})$

$I = (\dfrac{\sqrt 2+1}{\sqrt 2 +2}, \dfrac{\sqrt 2 +1 }{\sqrt 2 +2})$

Upon rationalizing the above terms, we get,

$I = (\dfrac{1}{\sqrt 2}, \dfrac{1}{\sqrt 2})$