# What is the orthocenter of a triangle with corners at #(2 ,0 )#, #(3 ,4 )#, and (6 ,3 )#?

The orthocenter of the triangle is :

Let

Let ,

Let

Now,

Now,

Putting ,

From

Hence, **the orthocenter of the triangle is :

**

Please see the graph.

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

First, find the slopes of the lines containing the sides of the triangle. Then, determine the slopes of the lines perpendicular to these sides (these are the altitudes). Next, find the equations of these perpendicular lines. Finally, solve the system of equations formed by these lines to find their point of intersection, which is the orthocenter.

Given the vertices (2, 0), (3, 4), and (6, 3), calculate the slopes of the lines passing through these points. Then, find the perpendicular slopes. Using these perpendicular slopes and the corresponding vertices, find the equations of the altitudes. Solve the system of equations formed by these lines to find their intersection point, which is the orthocenter.

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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.

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.

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.

- Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?
- What is the orthocenter of a triangle with corners at #(2 ,3 )#, #(6 ,1 )#, and (6 ,3 )#?
- What is the orthocenter of a triangle with corners at #(2 ,8 )#, #(3 ,4 )#, and (6 ,3 )#?
- Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically?
- How do you find the perpendicular bisectors of a triangle?

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