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

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

KnowledgeBoat · Accepted Answer

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, ⇒ OA² = OD² + AD² ⇒ (2a)² = a² + AD² ⇒ 4a² = a² + AD² ⇒ AD² = 4a² - a² ⇒ AD² = 3a² ⇒ 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).

Mathematics

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

Coordinate Geometry

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

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