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

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 )#?

1308 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-05T18:35:09

# (3,7)#.

Name the vertices as #A(3,6), B(3,2) and C(5,7)#.

Note that, #AB# is a vertical line, having the eqn. #x=3#.

So, If #D# is the foot of #bot# from #C# to #AB#, then,

#CD#, being #bot AB#, a vertical line, #CD# has to be a

horizontal line through #C(5,7)#.

Clearly, #CD : y=7#.

Also, #D# is the Orthocentre of #DeltaABC#.

Since, #{D}=ABnnCD, :., D=D(3,7)# is the desired

orthocentre!