The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates of the vertices.

Given equilateral triangle OAB. OA = OB = AB = 2a units. Draw AD ⊥ OB. In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side bisects the side. ∴ OD = x OB = x 2a = a. In right angle triangle OAD, ⇒ OA 2 = OD 2 + AD 2 ⇒ (2a) 2 = a 2 + AD 2 ⇒ 4a 2 = a 2 + AD 2 ⇒ AD 2 = 4a 2 - a 2 ⇒ AD 2 = 3a 2 ⇒ AD = units. ⇒ AD = a units. From graph, Co-ordinates of O = (0, 0) Co-ordinates of B = (2a, 0) As, OD = a units and AD = a units. Co-ordinates of A = (a, a). Hence, co-ordinates of O = (0, 0), B = (2a, 0) and A = (a, a).

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Mathematics

The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates of the vertices.

Coordinate Geometry

Related Questions

Write the co-ordinates of the vertices of a rectangle which is 6 units long and 4 units wide if the rectangle is in the first quadrant, its longer side lies on the x-axis and one vertex is at the origin.

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