Find the circumcentre of the triangle formed by the points (2,4),(2,6),(2+root3,5)
Answers
Answer:
Given three points A(2,3) , B(1,-5) and C(-1,4)
Mid point of AB=(
2
2+1
,
2
3−5
)=(
2
3
,−1)
Slope of AB=
x
2
−x
1
y
2
−y
1
=
1−2
−5−3
=
−1
−8
=8
∴ Slope of perpendicular bisector =
8
−1
∴ Equation of AB with respect to slope =
8
−1
and coordinate (
2
3
,−1)
y−y
1
=m(x−x
1
)
⇒y+1=
8
−1
(x
2
−3
)
y+1=
16
−1
(2x−3)⟹16y+16=−2x+3
2x+16y+13=0⟶(1)
Slope of =(
2
2−1
,
2
3+4
)=(
2
1
,
2
7
)
Slope of =
x
2
−x
1
y
2
−y
1
=
−1−2
4−3
=
3
−1
∴ Slope of perpendicular bisector =3
∴ Equation of AC with respect to slope and 3 coordinate (
2
1
,
2
7
)
⇒y−y
1
=m(x−x
1
)
y−
2
7
=3(x−
2
1
)
2y−7=6x−3
⇒6x−2y+4=0
∴3x−y+2=0⟶(2)
2x+16y=−13⟶×3
3x−y=−2⟶×2
50y=−35
6x+48y=−39−6x±2y=±−4
∴y=
50
−35
=
10
−7
∴x=
10
−9
∴ The circumcenter of triangle =(
10
−9
,
10
−7
)Step-by-step explanation: