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If (3, 2) and (-3, 2) are two vertices of anequilateral triangle which contains the origin,find the third vertex.[Board Term-2, 2012 Set (12)] |
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Answer» Let an equilateral triangleΔ ABC : AB = BC = AC.vertices are A(3,2) and B(-3,2) and C(x,y).The mid point of the side AB is M (0,2).(AB)²= (3+3)² +(2-2)² = 6² + 0² =36AB = 6 cmAB = BC = AC = 6 unit.AM = 3 unit.As two vertices are A(-3,2) and B(3,0) so that Third vertex will be atY-axis(x=0).so thatThird vertex C(0,y) and it is located below the origin.Hence it contains the origin.Now, y² = (AC)² -(AM)²⇒ y² = 6² - 3² = 36 - 9 =27 y =√27 = 3√3 unitHence Third vertices of the triangleare A(-3,2) , B(3,2) and C(0,3√3). |
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