Prove that the lines , y = 4 and form an equilateral triangle.

Given: equations are as follows:


y = √3 x + 1……(1)


y = 4 …….(2)


y = - √3 x + 2…….(3)


Assuming:


In triangle ABC, let equations (1), (2) and (3) represent the sides AB, BC and CA, respectively.


To prove:


Lines y = √3 x + 1, y = 4 and y = - √3 x + 2 form an equilateral triangle.


Explanation:


Solving (1) and (2):


x = √3 , y = 4


Thus, AB and BC intersect at B(√3,4)


Solving (1) and (3):



Thus, AB and CA intersect at A(,)


Similarly, solving (2) and (3):


, y = 4


Thus, BC and AC intersect at C(,4)


Now, we have:





Hence Proved, the given lines form an equilateral triangle


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