The base QR of an equilateral triangle PQR lies on x – axis. The coordinates of the point Q are (– 4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.


Let QR be the base


Since origin is mid – point O(0,0) of QR


Then the coordinates of R(x,y) is given by


(– 4 + x)/2 = 0


x = 4


(0 + y)/2 = 0


y = 0


R(4,0)


Distance of QR = √(4 + 4)2 + 0


QR = 8


PR = 8


Let P(x,y)


8 = √(4 – x)2 + (0 – y)2


64 = 16 + x2 – 8x + y2


Since it will lie on x axis


× = 0


64 = 16 + y2


48 = y2


y = 4√3 or – 4√3


Hence,


P(0, 4√3) or P(0, – 4√3) and R(4, 0)


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