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Let ABC be a triangle, two of whose
vertices are (15, 0) and (0, 10). If the
orthocentre is (6, 9),then the third
vertex is
Daer Asham,
orthocenter is the intersection of the 3 altitudes of a circle.for example, the coordinates of the vertices of the triangle are A(a, b), B(c, d) and C(e, f)first, get the equation of the line passing through C and is perpendicular to AB. (altitude to AB)then, get the equation of the line passing through A and is perpendicular to BC. (altitude to BC)then, find the intersection of these lines. (the altitude to AC will also pass through this point since the altitude of a triangle are concurrent to each other - meaning 3 or more lines intersecting at a point...)the intersection is the coordinates of the orthocenter :Dcentroid is the intersection of the medians of a triangle(median - line connecting a vertex of a triangle and the midpoint of the side opposite to it.)the coordinates of the midpoint of a triangle with vertices at (a, b), (c, d), (e, f) are ( (a+c+e)/3, (b+d+f)/3 )circumcenter - the intersection of the 3 perpendicular bisectors of a triangle(perpendicular bisector - a line perpendicular to a side of a triangle passing through its midpoint)this point is equidistant to the vertices of the triangle.btw, there is another "center" thing related to triangles...incenter - intersection of the angle bisectors of a triangle(angle bisector - lines bisecting the angles of a triangle)the incenter is equidistant from the sides of the triangle
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Thanks
Aman Bansal
Askiitian Expert
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