Math, asked by akshayamanoj9, 8 months ago

PQR is an equilateral triangle with coordinates Q(0,6) , R(0,-6) . Find the coordinates of the vertex
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Answers

Answered by mysticd
3

Given , PQR is an equilateral triangle with coordinates Q(0,6) , R(0,-6)

Let Coordinates of point P ( x ,y ).

 i) mid-point \: of \: QR

 = \Big(\frac{x_{1}+x_{2}}{2} , \frac{x_{1}+x_{2}}{2}\Big)

 = \Big( \frac{0+0}{2}, \frac{6-6}{2}\Big)

 = M( 0,0)

/* Distance formula */

ii) QR^{2}

= ( 0 - 0 )^{2} + ( -6 - 6 )^{2}

 = (-12)^{2}

 \therefore QR = 12 \: units

 iii) Height \: of \: the \: \triangle PQR

 PM = y = \frac{\sqrt{3}}{2} \times QR

 = \frac{\sqrt{3}}{2} \times 12

 = 6\sqrt{3}

Therefore.,

 \red{ Coordinates of point P ( x ,y )}\green {= ( 0,6\sqrt{3})}

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