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).

Three vertices of a square are A(2, 3), B (-3, 3) and C (-3, -2). Plot these points on a graph paper and hence use it to find the co-ordinates of the fourth vertex. Also find the area of the square.

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In the adjoining figure, ABCD is a rectangle with length 6 units and breadth 3 units. If O is the mid-point of AB, find the coordinates of A, B, C and D.

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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

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