If two vertices of an equilateral triangle are (-2,1) and (8,-1) find the third vertex with positive cordinates
Answers
Answered by
0
Answer:
Points A(−1,0) and B(1,0) lie on x-axis.
Mid-point of AB is (0,0).
Clearly, point C lies on y-axis. Since, it lies above y-axis.
So, let the coordinates of point C be (0,k).
Coordinates of centroid G is (0,
3
k
).
We also know that circumcenter, centroid and incenter of the equilateral triangle coincides.
Hence, the coordinates of circumcenter is (0,
3
k
).
Since, ABC is equilateral triangle,
AB=AC
⇒(AB)
2
=(AC)
2
⇒k=
3
So, the coordinates of circumcenter is (0,
3
1
).
Radius CG=
3
2
Equation of circumcircle is
(x−0)
2
+(y−
3
1
)
2
=
3
4
⇒x
2
+y
2
−
3
2
y−1=0
⇒
3
(x
2
+y
2
)−2y−
3
=0
Answered by
1
Answer:
hope this answer helps you
Attachments:
Similar questions