First slide

Cartesian plane

Question

One vertex of the equilateral triangle with centroid at the origin and one side as $x + y - 2 = 0$ , is

Moderate

A

(-1,1)
B

{2,2)
C

(-2,-2)
D

none of these

Solution

Since the triangle is equilateral. Therefore, centroid coincides with the circumcentre and orthocentre. The equation of the perpendicular bisector of $x + y - 2 = 0$ and passing through the centroid (0, 0) is $x - y = 0$ The vertex of the triangle must lie on $x - y = 0$ and the origin and the vertex must lie on the same side of $x + y - 2 = 0 .$ So, we can choose (- 2, - 2) as the vertex

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