Question

A(-3, 0)and B (3, 0) are the vertices of an equilateral ABC. Find the coordinates of C.​

Answer 1

Answer:

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Answer 2

Answer:

C(3√3 ,0) and C(−3√3 ,0)

Step-by-step explanation:

Let the third vertex of the equilateral ΔABC be C(x,y)

So by distance formula we have,

Distance between two points = √(x 2 −x 1 ) ^2+(y 2 −y1 ) ^2

∴BC= √(0−0)^ 2 +(3+3)^2 = √6^2 = √36 = 6

∴AB= √(x−0) ^2 +(y+3) ^2

⇒AB ^2 =x^2 +y^2 +2y=27 -----(1)

Now, AC= √(x−0) ^2 +(y−3) ^2

⇒AC^2 =x^2 +y^2 +9−6y = 36

⇒27−2y−6y+9=36⇒−8y=36−36

⇒y=0

∴x^2 =27

⇒x = √27 = √ 3×3×3 x = + 3√3 or−3√3

∴ Required points are C(3√3 ,0) and C(−3√3 ,0)

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