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Question: If (x<sub>i</sub>, y<sub>i</sub>) , i = 1, 2, 3 are vertices of equilateral triangle such that (x<su...

If (xi, yi) , i = 1, 2, 3 are vertices of equilateral triangle such that (x1 + 2)2 + (y1 – 3)2 = (x2 + 2)2 + (y2 –3)2

= (x3 +2)2 + (y3 –3)2 then value of x1+x2+x3y1+y2+y3\frac{x_{1} + x_{2} + x_{3}}{y_{1} + y_{2} + y_{3}} is:

A

23\frac{2}{3}

B

–23–\frac{2}{3}

C

32\frac{3}{2}

D

–32–\frac{3}{2}

Answer

–23–\frac{2}{3}

Explanation

Solution

From given condition we can say circumcentre is point (– 2, 3)

but triangle is equilateral so centroid is (– 2, 3)

Ž x1+x2+x33\frac{x_{1} + x_{2} + x_{3}}{3} = – 2, y1+y2+y33\frac{y_{1} + y_{2} + y_{3}}{3} = 3

Ž x1+x2+x3y1+y2+y3\frac{x_{1} + x_{2} + x_{3}}{y_{1} + y_{2} + y_{3}} = – 23\frac{2}{3}