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Understanding Triangle Geometries: Intersection of Medians and Orthocenter Coordinates

This document explores key concepts in triangle geometry, including finding the intersection point of medians and identifying the orthocenter's coordinates for given triangles. It answers various mathematical questions, including the length of sides, types of triangles (like obtuse and equilateral), and the area calculation for given vertices. Additionally, it discusses the conditions for triangle formation based on side lengths and provides algebraic problem-solving within triangular contexts.

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Understanding Triangle Geometries: Intersection of Medians and Orthocenter Coordinates

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  1. Answer: no Question: A triangle has vertices A(4, 4), B(8,10), and C(12,4) Determine the point of intersection of the medians, and state its coordinates.

  2. Answer: d Question: Find the coordinates of the orthocenter of the following triangle.

  3. Answer: (8,6) Question: If A(3,2) and B(5,-10), find the length of AB.

  4. Answer: 19 Question: In what type of triangle is the orthocenter outside of the triangle?

  5. Answer: Obtuse Question: Triangle PQR is a right scalene triangle. If angle Pis the right angle in triangle PQR, which of the following is a valid conclusion? a. b. c. d.

  6. Answer: (0, 0) Question: Triangle JKL is an equilateral triangle, and triangle VUT is its mid-segment triangle. Which of the following is true? a. b. c. d.

  7. Answer: Question: Find the area of a triangle that has points A(0,4), B(-3,0), and C(3,0).

  8. Answer: right • Question: Is it possible to make a triangle with side lengths 3 in, 4 in, and 7 in?

  9. Answer: 12 Question: Let BD= 2x +6 and AE= 5x -7. Given B is the midpoint of side CA, and D is the midpoint of side CE, find the value of x.

  10. Answer: a Question: If the perimeter of the triangle is 40. Is the following triangle possible? 4x + 5

  11. Answer: 11 Question: If J(-4,0), E(-2, -4), N(2, -2) Classify triangle JEN by its angles.

  12. 5x+ 11˚ 7x - 8˚ 3x + 12˚ Answer: yes Question: Find the value of x.

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