SATHEE: Straight Line and Pair of Straight Lines 1 Question 22

Straight Line and Pair of Straight Lines 1 Question 22

22. 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

(2013 Main)

(a) $2 + \sqrt{2}$

(b) $2 - \sqrt{2}$

(c) $1 + \sqrt{2}$

(d) $1 - \sqrt{2}$

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Solution:

Given mid-points of a triangle are $(0, 1), (1, 1)$ and $(1, 0)$ . Plotting 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. $2 \sqrt{2}$ .

$x$ -coordinate of incentre $= \frac{2 \times 0 + 2 \sqrt{2} \cdot 0 + 2 \cdot 2}{2 + 2 + 2 \sqrt{2}}$

$= \frac{2}{2 + \sqrt{2}} \times \frac{2 - \sqrt{2}}{2 - \sqrt{2}} = 2 - \sqrt{2}$

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Straight Line and Pair of Straight Lines 1 Question 22

22. 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

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22. 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