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

Triangle with vertices at

Orthocenter =

Given:

Vertices at

We have three vertices:

We will find the slope using the vertices

Let

Formula to find the slope (m) =

We need a perpendicular line from the vertex

Perpendicular slope is

Use the Point-Slope Formula to find the equation.

Point-slope formula:

Hence,

We will repeat the process from

Consider side

Next, we find the slope.

Find the perpendicular slope.

Point-slope formula:

Hence,

Find the solution to the system of linear equations to find the vertices of the Orthocenter of the triangle.

The solution is becoming too long. Method of Substitution will provide solution for the system of linear equations.

Orthocenter

The construction of the triangle with the Orthocenter is:

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The orthocenter of the triangle with vertices at (3, 1), (1, 6), and (5, 2) is located at the point (3, 3).

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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?
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