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The coordinates of the third vertex of an equilateral triangle whose two vertices are at (3, 4), (–2, 3) are ________.
  • a)
    (1, 7)
  • b)
    (5, 1)
  • c)
  • d)
    (– 5, 5)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The coordinates of the third vertex of an equilateral triangle whose t...
Since, ΔABC is equilateral.
∴ AB = AC ⇒ AB2 = AC2

⇒ (x – 3)2 + (y – 4)2
= (x + 2)2 + (y – 3)2
⇒ 5x + y – 6 = 0 ... (i)
Now, area of equilateral triangle = 
∴ Area of ΔABC = 

⇒ x – 5y = 13√3 − 17 ...(ii)
or x – 5y = −(13√3 + 17) ...(iii)
Solving (i) and (ii), we get,

Also, on solving (i) and (iii), we get
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