Question

The co-ordinate of the circumcentre of triangle ABC with vertices A(3,0), B(-1,-6) and C(4, -1) is
a) (1,-3)
b) (-1,3)
c) (3,-2)
d) (-2,3)

Answer 1

Reply quickly, plzzzzzzzzzz

Answer 2

make the co-ordiniate of the circumcentre O (x,y)

make E(1,-3), F(1.5,-3.5)
vector AB=(-4,-6)
vector BC=(5,5)
vector OE=(1-x,-3-y)
vector OF=(1.5-x, -3.5-y)
since AB and OE are perpendicular
since BC and OF are perpendicular
so vector AB * vector OE=0
so vector BV * vector OF =0
so (-4(1-x)+(-6)(-3-y)=0
(5(1.5-x)+(5)(-3.5-y)=0
get x and y

Answer 3

x=1, y=-3

Answer 4

so the coordinate of the circumcentre of triangle ABC is (1,-3)