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If two vertices of a equilateral triangle be (0,0).(3,√3) find the third vertices |
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Answer» Two vertices of an equilateral triangle are (0, 0) and (3, √3).Let the third vertex of the equilaterla triangle be (x, y)Distance between (0, 0) and (x, y) = Distance between (0, 0) and (3, √3) = Distance between (x, y) and (3, √3)√(x2\xa0+ y2) = √(32\xa0+ 3) = √[(x - 3)2\xa0+ (y - √3)2]x2\xa0+ y2\xa0= 12x2\xa0+ 9 - 6x + y2\xa0+ 3 - 2√3y = 1224 - 6x - 2√3y = 12- 6x - 2√3y = - 123x + √3y = 6x = (6 - √3y) / 3⇒ [(6 - √3y)/3]2\xa0+ y2\xa0= 12⇒ (36 + 3y2\xa0- 12√3y) / 9 + y2\xa0= 12⇒ 36 + 3y2\xa0- 12√3y + 9y2\xa0= 108⇒ - 12√3y + 12y2\xa0- 72 = 0⇒ -√3y + y2\xa0- 6 = 0⇒ (y - 2√3)(y + √3) = 0⇒ y = 2√3 or - √3If y = 2√3, x = (6 - 6) / 3 = 0If y = -√3, x = (6 + 3) / 3 = 3So, the third vertex of the equilateral triangle = (0, 2√3) or (3, -√3). (0,4) |
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