if (0,0)and (3,3) are two vertics of an equilateral triangle then find third vertex
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Answer:
Two vertices of an equilateral triangle are (0,0)and(3,√3).
Let the third vertex of the equilateral triangle be (x,y)
Distance between (0,0)and(x,y) = Distance between(0,0)and(3,√3) = Distance between (x,y)and(3,√3)
(x
2
+y
2
)
=
(3
2
+3)
=
(x−3)
2
+(y−
3
)
2
x
2
+y
2
=12
x
2
+9−6x+y
2
+3−2
3y
=12
24−6x−2
3y
=12
−6x−2
3y
=−12
3x+
3y
=6
x=
3
6−
3y
3
(6−
3y
)
2+y
2
=12
9
(36+3y2−12
3y
)
+y
2
=12
36+3y
2
−12
3y
+9y2=108
−12
3y
+12y
2
−72=0
−3y
+y2−6=0
(y−2
3
)(y+
3
)=0
y=2
3
or
−3
Ify=2
3
,x=(6−6)/3=0
Ify=−
3
,x=
3
9
=3
So,the third vertex of the equilateral triangle=(0,2
3
)or(3,−
3
).
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