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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?
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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
∴ 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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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?
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