The x and y coordinate of the centroid are given by:īelow is shown the graphical solution including triangle, the medians of the three vertices and their point of intersection O called the centroid. ( (a x A + b x B + c x C ) / (a + b + c), (a y A + b y B + c y C ) / (a + b + c))įind the centroid of a triangle whose vertices are A(-2, 0), B(4, 3) and C(1, 6).įind the incenter of a triangle whose vertices are A(- 1, 0), B(3, 3) and C(3, - 3).įind the orthocenter of a triangle whose vertices are A(0, 0), B(5, 0) and C( 3, 3) If A(x A, y A), B(x B, y B) and C(x C, y C) are the vertices of a triangle with sides of lengths a, b and c opposite vertices A, B and C respectively, then the incenter is at:

The angle bisector of a triangle is a line segment from a given vertex that divide the interior angle at the vertex into two equal angles. Which are the averages of the x and y coordinates of the vertices. X = (x A + x A + x A ) / 3, y = (y A + y B + y C ) / 3 For any triangle, all three altitudes intersect at a point called the centroid of the triangle.įor a triangle with vertices A(x A, y A), B(x B, y B) and C(x C, y C), then the centroid is at: The median of a triangle is a line segment from a given vertex to the middle of the opposite side. For any triangle, all three altitudes intersect at a point called the orthocenter which may be inside or outside the triangle.Įxample of triangle with othocenter inside the triangle.Įxample of triangle with othocenter outside the triangle. The altitude of a triangle is a line through a given vertex of the triangle and perpendicular to the side opposite to the vertex. The altitudes, medians and angle bisectors of a Triangle are defined and problems along with their solutions are presented. Altitudes, Medians and Angle Bisectors of a Triangle

Definition of altitude geometry