If the points (0,0),(3,3),(p,q) form an equilateral triangle and q1, q2 are the two values of q then q1+q2=

Third vertex=x1+x2±3y1−y22,y1+y2∓3x1−x22=0+3±3(0−3)2,0+3∓3(0−3)2=q1+q2=y1+y2=0+3=3

If the points (0,0),(3,3),(p,q) form an equilateral triangle and q1, q2 are the two values of q then q1+q2=

Third vertex=x1+x2±3y1−y22,y1+y2∓3x1−x22=0+3±3(0−3)2,0+3∓3(0−3)2=q1+q2=y1+y2=0+3=3

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If the points $(0, 0), (3, \sqrt{3}), (p, q)$ form an equilateral triangle and q₁, q₂ are the two values of q then $q_{1} + q_{2} =$

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$\sqrt{3}$

$2 \sqrt{3}$

$- \sqrt{3}$

answer is B.

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Detailed Solution

Third vertex

$= (\frac{x_{1} + x_{2} \pm \sqrt{3} (y_{1} - y_{2})}{2}, \frac{y_{1} + y_{2} \mp \sqrt{3} (x_{1} - x_{2})}{2})$

$= (\frac{0 + 3 \pm \sqrt{3} (0 - \sqrt{3})}{2}, \frac{0 + \sqrt{3} \mp \sqrt{3} (0 - 3)}{2})$

$= q_{1} + q_{2} = y_{1} + y_{2} = 0 + \sqrt{3} = \sqrt{3}$

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If the points (0,0),(3,3),(p,q) form an equilateral triangle and q1, q2 are the two values of q then q1+q2=

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If the points $(0, 0), (3, \sqrt{3}), (p, q)$ form an equilateral triangle and q₁, q₂ are the two values of q then $q_{1} + q_{2} =$