First slide

Cartesian plane

Question

If the points $A (1, 1), B (- 1, - 1)$ and $C (\sqrt{3}, \sqrt{3})$ are the vertices of a triangle, then triangle is

Easy

A

right-angled
B

isosceles
C

equilateral
D

none of these

Solution

We have,
$A B = 2 \sqrt{2}, B C = \sqrt{(\sqrt{3} - 1)^{2} + (\sqrt{3} + 1)^{2}} = 2 \sqrt{2}$
and , $A C = \sqrt{(\sqrt{3} + 1)^{2} + (\sqrt{3} - 1)^{2}} = 2 \sqrt{2}$
$∴ A B = B C = C A$
So $△ A B C$ is equilateral.

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