First slide

Cartesian plane

Question

The in centre of the triangle with vertices $(1, \sqrt{3)}, (0, 0)$ and (2,0) is

Moderate

A

$(1, \sqrt{3} / 2)$
B

$(2 / 3, 1 / \sqrt{3})$
C

$(2 / 3, \sqrt{3} / 2)$
D

$(1, 1 / \sqrt{3})$

Solution

Let the vertices of the triangle be $A (1, \sqrt{3})$ , B (0, 0) and C (2, 0). We observe that
$A B = 2 = B C = A C$
So, the triangle is equilateral. Consequently, its incentre coincides with the centroid whose coordinates are.
$(\frac{1 + 0 + 2}{3}, \frac{\sqrt{3} + 0 + 0}{3}) = (1, \frac{1}{\sqrt{3}})$

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