The incentre of the triangle with vertices $(1, \sqrt{3}), (0,0)$ and $ (2,0) is $
- $\Big(1, \frac{\sqrt{3}}{2}\Big)$
- $\Big(\frac{2}{3} \frac{1}{\sqrt{3}}\Big)$
- $\Big(\frac{2}{3} \frac{\sqrt{3}}{2}\Big)$
- $\Big(1,\frac{1}{\sqrt{3}}\Big)$
The Correct Option is D
Solution and Explanation
Therefore, it is an equilateral triangle. So, the in centre coincides with centroid.
$\therefore \hspace25mm I\equiv \Bigg(\frac{0 + 1 + 2}{3},\frac{0+0+\sqrt{3}}{3}\Bigg)$
$\Rightarrow \hspace25mm I \equiv(1/\sqrt{3})$
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Concepts Used:
Coordinates of a Point in Space
Three-dimensional space is also named 3-space or tri-dimensional space.
It is a geometric setting that carries three values needed to set the position of an element. In Mathematics and Physics, a sequence of ‘n’ numbers can be acknowledged as a location in ‘n-dimensional space’. When n = 3 it is named a three-dimensional Euclidean space.
The Distance Formula Between the Two Points in Three Dimension is as follows;
The distance between two points P1 and P2 are (x1, y1) and (x2, y2) respectively in the XY-plane is expressed by the distance formula,
Read More: Coordinates of a Point in Three Dimensions