Given the three points A = [1,4], B = -5, -1] and C = [6,-3], consider...

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Given the three points A = [1,4], B = -5, -1] and C = [6,-3], consider the triangle the point on AC so that BM is the altitude through B perpendicular to AC. Likewise let N that CN is the altitude through C perpendicular to AB. i) Find M ii) Find N: B L M= H N H= M (diagram not to scale) N= is entered as [1/2, 3/4]. A Note: in Maple notation the point [ 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 AA ABC, and let M be be the point on AB so Given the three points A = [1,4], B = -5, -1] and C = [6,-3], consider the triangle the point on AC so that BM is the altitude through B perpendicular to AC. Likewise let N that CN is the altitude through C perpendicular to AB. i) Find M ii) Find N: B L M= H N H= M (diagram not to scale) N= is entered as [1/2, 3/4]. A Note: in Maple notation the point [ 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 AA ABC, and let M be be the point on AB so