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

##### 1 Answer

Triangle with **vertices** at

**Orthocenter = **

#### Explanation:

**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**, which is the **opposite reciprocal** of our slope

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:**