Question

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

Answer 1

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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