Math Problem Statement

Triangle with vertices at A (-6, -2), B (0,6), and C (6,0). Draw this triangle. The point of concurrency of these three lines is the orthocenter of the triangle. Label it P.

Solution

Here is the triangle with vertices A (-6, -2), B (0, 6), and C (6, 0), and the orthocenter labeled as point P.

Would you like me to go over how the orthocenter is calculated or provide further details on the properties of the triangle?

Here are 5 related questions you might find interesting:

  1. What is the definition of the orthocenter in a triangle?
  2. How do you find the altitude of a triangle geometrically?
  3. What is the relationship between the orthocenter and the circumcenter?
  4. How do you calculate the area of this triangle?
  5. Can the orthocenter ever lie outside the triangle?

Tip: The orthocenter's position relative to the triangle changes based on the type of triangle: it lies inside for acute triangles, on the vertex for right triangles, and outside for obtuse triangles.

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Math Problem Analysis

Mathematical Concepts

Geometry
Triangles
Orthocenter
Altitude

Formulas

Equation of the altitude in a triangle

Theorems

Properties of the orthocenter in a triangle

Suitable Grade Level

Grades 9-12