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ABC is a equilateral triangle with coordinates of B (1,0) and C(5,0). Find the co-ordinates of vertex A. (Can you please explain how to do this type questions.)

ABC is a equilateral triangle with coordinates of B (1,0) and C(5,0). Find the co-ordinates of vertex A. (Can you please explain how to do this type questions.)
 

Grade:10

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
10 years ago
Hello student,
Please find the answer to your question below
Givencoordinates of B (1,0) and C(5,0)
Let coordinates of A be (a,b)
In an equilateral triangle the lengths of all sides will be equal
So BC=\sqrt{(1-5)^{2}+(0-0)^{2}}=4
So AB=CA=4
AB=\sqrt{(a-1)^{2}+(b-0)^{2}}=4
Squaring on both sides we get
(a-1)2+b2=16
a2+b2-2a-15=0.......(1)
Also CA=\sqrt{(5-a)^{2}+(b-0)^{2}}=4
Squaring on both sides we get
(5-a)2+b2=16
a2+b2-10a+9=0........(2)
(1)-(2) gives we get 8a-24=0
So a=3
Substituting a=3 in equation 1 we get b2=12 So b=2\sqrt{3}
So vertex A is (3,2\sqrt{3})

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