Given the three points A 2 6 B 4 6 and C 4 1 consider...

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Geometry

Given the three points A 2 6 B 4 6 and C 4 1 consider the triangle AABC and let M be the point on AC so that BM is the altitude through B perpendicular to AC Likewise let N be the point on AB so that CN is the altitude through C perpendicular to AB B i Find M ii Find N M N M diagram not to scale N Note in Maple notation the point is entered as 1 2 3 4 Challenge worth 2 points iii It is known that the three altitudes of any triangle meet at a common point called the orthocenter For AABC this orthocenter is

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Given the three points A 2 6 B 4 6 and C 4 1 consider the triangle AABC and let M be the point on AC so that BM is the altitude through B perpendicular to AC Likewise let N be the point on AB so that CN is the altitude through C perpendicular to AB B i Find M ii Find N M N M diagram not to scale N Note in Maple notation the point is entered as 1 2 3 4 Challenge worth 2 points iii It is known that the three altitudes of any triangle meet at a common point called the orthocenter For AABC this orthocenter is