Question

If the centroid and circumcenter of a triangle are
(3,3) and (6,2) respectively then the orthocenter
is?​

Answer 1

Answer:

n any triangle, orthocentre, centroid, and circumcentre are collinear and centroid divides the line joining orthocentre and circumcenter in ratio 2:1

Let the orthocentre be (x,y)

Using the section formula, if a point

(x,y) divides the line joining the points (x

1

,y

1

) and

(x

2

,y

2

) in the ratio m:n, then (x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

Substituting (x

1

,y

1

)=(x,y) and (x

2

,y

2

)=(6,2) and m=2,n=1 in the section formula, we get the centroid

=(

2+1

2(6)+1(x)

,

2+1

2(2)+1(y)

)=(

3

x+12

,

3

y+4

)

Given

centroid =(3,3)

=>(

3

x+12

,

3

y+4

)=(3,3)

=>

3

x+12

=3;

3

y+4

=3

x+12=9;y+4=9

x=−3;y=5

Hence, orthocentre =(−3,5)

Answer 2

Answer:

mark as a brainlist answer..