What is the orthocenter of a triangle with corners at #(2 ,3 )#, #(6 ,1 )#, and (6 ,3 )#?

Question

What is the orthocenter of a triangle with corners at #(4 ,1 )#, #(1 ,3 )#, and (5 ,2 )#?
What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,3 )#, and (5 ,2 )#?
What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,6 )#, and (5 ,2 )#?
What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(1 ,6 )#, and (2 ,2 )#?
What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,2 )#?
What is the orthocenter of a triangle with corners at #(3 ,1 )#, #(4 ,5 )#, and (2 ,7 )#?
What is the orthocenter of a triangle with corners at #(3 ,2 )#, #(4 ,5 )#, and (2 ,7 )#?
What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(4 ,5 )#, and (2 ,9 )#?
What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(2 ,5 )#, and (7 ,9 )#?
What is the orthocenter of a triangle with corners at #(6 ,3 )#, #(2 ,4 )#, and (7 ,9 )#?

1854 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-16T13:31:59

Hence, the orthocentre of #triangle ABC# is #C(6,3)#

Let , #triangle ABC # ,be the triangle with corners at

#A(2,3) ,B(6,1) and C(6,3) # .

We take, #AB=c, BC=a and CA=b#

So,

#c^2=(2-6)^2+(3-1)^2=16+4=20#

#a^2=(6-6)^2+(1-3)^2=0+4=4#

#b^2=(2-6)^2+(3-3)^2=16+0=16#

It is clear that, #a^2+b^2=4+16=20=c^2#

# i.e. color(red)(c^2=a^2+b^2=>mangleC=pi/2#

Hence, #bar(AB)# is the hypotenuse.

#:.triangle ABC # is the right angled triangle.

#:.#The orthocenter coindes with #C#

Hence, the orthocentre of #triangle ABC# is #C(6,3)#

Please see the graph:

enter image source here