Lesson Sum of vectors connecting the center of mass of a triangle with its vertices
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<H2>Sum of vectors connecting the center of mass of a triangle with its vertices</H2> Prove yourself that <B>for any triangle in a plane the sum of the vectors connecting the center of mass of the triangle with its vertices is equal to zero</B>. In a coordinate plane, the center of mass of a triangle with vertices <B>P</B>=<B>P</B>(x1,y1), <B>Q</B>=<B>Q</B>(x2,y2) and <B>R</B>=<B>R</B>(x3,y3) is the point with the coordinates {{{x[0]}}} = {{{(x[1]+x[2]+x[3])/3}}}, {{{y[0]}}} = {{{(y[1]+y[2]+y[3])/3}}}. The center of mass of a triangle is called sometimes a <B>centroid</B> or a <B>barycenter</B> of the triangle. <B>Tip</B>: Use the component form of vectors in a coordinate plane (see the lessons <A HREF=http://www.algebra.com/algebra/homework/Vectors/Vectors-in-a-coordinate-plane.lesson>Vectors in a coordinate plane</A> and <A HREF=http://www.algebra.com/algebra/homework/Vectors/Addition-Subtraction-and-Multiplication-by-a-number-of-vectors-in-a-coordinate-plane.lesson>Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane</A> under the topic <B>Introduction to vectors, addition and scaling</B> of the section <B>Algebra-II</B> in this site). If you want to see this <B>Problem</B> solved, find the solution in the lesson <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-from-the-center-of-mass-of-the-n-sided-polygon-to-its-vertices.lesson>Sum of vectors connecting the center of mass of a n-sided polygon with its vertices</A> under the topic <B>Introduction to vectors, addition and scaling</B> of the section <B>Algebra-II</B> in this site. <B>Note</B>. For any triangle, the center of mass coincides with the intersection point of the triangle's medians. This is proved in the lesson <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-triangle-is-the-Intersection-point-of-its-medians.lesson>The Centroid of a triangle is the Intersection point of its medians</A> under the topic  <B>Geometry</B> of the section <B>Word problems</B> in this site. My introductory lessons on vectors in this site are - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Vectors-in-a-plane.lesson>Vectors in a plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-are-coherently-oriented-sides-of-a-convex-closed-polygon.lesson>Sum of vectors that are coherently oriented sides of a convex closed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-are-coherently-oriented-sides-of-an-unclosed-polygon.lesson>Sum of vectors that are coherently oriented sides of an unclosed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-that-connect-the-center-of-a-parallelogram-with-its-vertices.lesson>Sum of vectors that connect the center of a parallelogram with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Vectors-in-a-coordinate-plane.lesson>Vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Addition-Subtraction-and-Multiplication-by-a-number-of-vectors-in-a-coordinate-plane.lesson>Addition, Subtraction and Multiplication by a number of vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Summing-vectors-that-are-coherently-oriented-sides-of-a-convex-closed-polygon.lesson>Summing vectors that are coherently oriented sides of a convex closed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Summing-vectors-that-are-coherently-oriented-sides-of-an-unclosed-polygon.lesson>Summing vectors that are coherently oriented sides of an unclosed polygon</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-triangle-is-the-Intersection-point-of-its-medians.lesson>The Centroid of a triangle is the Intersection point of its medians</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-parallelogram-is-the-Intersection-point-of-its-diagonals.lesson>The Centroid of a parallelogram is the Intersection point of its diagonals</A> - Sum of vectors connecting the center of mass of a triangle with its vertices (this lesson) - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Sum-of-the-vectors-connecting-the-center-of-mass-of-a-quadrilateral-with-its-vertices.lesson>Sum of vectors connecting the center of mass of a quadrilateral with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-the-vectors-from-the-center-of-mass-of-the-n-sided-polygon-to-its-vertices.lesson>Sum of vectors connecting the center of mass of a n-sided polygon with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Sum-of-vectors-connecting-the-center-of-a-regular-polygon-with-its-vertices.lesson>Sum of vectors connecting the center of a regular n-sided polygon with its vertices</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-vectors-in-a-plane.lesson>Solved problems on vectors in a plane</A> - <A HREF=http://www.algebra.com/algebra/homework/Vectors/Solved-problems-on-vectors-in-a-coordinate-plane.lesson>Solved problems on vectors in a coordinate plane</A> - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-find-the-length-of-the-vector-in-a-coordinate-plane.lesson>HOW TO find the length of the vector in a coordinate plane</A> - <A HREF=https://www.algebra.com/algebra/homework/Vectors/Flying-airplane-blowing-wind-airspeed-groundspeed-etc.lesson>Flying airplane, blowing wind, airspeed, groundspeed etc.</A> - <A HREF=https://www.algebra.com/algebra/homework/Vectors/REVIEW-of-Introductory-lessons-on-vectors-in-a-plane.lesson>OVERVIEW of Introductory lessons on vectors in a plane</A> Use this file/link <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A> to navigate over all topics and lessons of the online textbook ALGEBRA-II.
