If two vertices of an equilateral triangle be are (0,0) adn (3,root 3)
Answers
unknown point is either (0,2√3) or (3,-√3)
let unknown point of equilatral triangle is (x, y)
we know equilatral triangle all side length are equal.
using distance formula
e.g. if two point (a, b) and (r, s) given distance between = √[(a-r)^2+(b-s)^2]
if A (0,0) B (3, √3) C (x, y) points of triangle .
then AB = BC = CA
also AB² = BC² = CA²
(0-3)² + (0- √3)2 = (3-x)²+ (√3-y)² =(x-0)² + (y-0)²
x^2+y^2=9 + 3 = 12
x^2 +y^2 =12 --------(1)
(3-x)^2+(√3-y)² =12
9+x^2 -6x +3+y^2-2√3 y=12
(x^2+y^2) + 12-6x-2√3 y=12
(x^2+y^2)=6x+2√3 y
put equation (1) value
12=6x+2√3 y----------(2)
solve equation (1) and (2)
put equation (1) y=(12-6x)/2√3
x^2+(12-6x)/12=12
=>12 x^2+(12-6x)^2=144
=> 12x^2+36x^2+144-144x=144
=> 48x^2-144x=0
=> x=0,3
so, y=12/2√3=2√3
y=-√3
hence unknown point is either (0,2√3) or (3,-√3)
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If two vertices of an equilateral triangle be (0,0) (3,root3) find the third vertex
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