Home > Geometry > Altitudes

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

Answer 1

Sadie Adams

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:

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Mason Adams

To find the orthocenter of a triangle, you need to find the point where the altitudes of the triangle intersect. The altitude is a line segment from one vertex perpendicular to the opposite side.

Step 1: Find the slopes of the lines passing through each side of the triangle. Step 2: Find the equations of the perpendicular lines passing through each vertex. Step 3: Find the intersection point of these lines, which will be the orthocenter.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.