Q. 54.0( 6 Votes )
Prove that the lines 
, y = 4 and 
form an equilateral triangle.
Answer :
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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