Pre-Calculus Homework Solutions 110

Pre-Calculus Homework Solutions 110 - Since MNP is...

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8. Given: n ABC is a right triangle with hypotenuse B w C w . M is the midpoint of B w C w . Prove: M is equidistant from the vertices. Proof: The coordinates of M ,the midpoint of B w C w , will be 1 } 2 2 c } , } 2 2 b } 2 5 ( c , b ). The distance from M to each of the vertices can be found using the Distance Formula. MB 5 Ï ( c 2 0 w ) 2 1 ( b w 2 2 b ) w 2 w 5 Ï c 2 1 b w 2 w MC 5 Ï ( c 2 2 w c ) 2 1 ( w b 2 0) w 2 w 5 Ï c 2 1 b w 2 w MA 5 Ï ( c 2 0 w ) 2 1 ( b w 2 0) 2 w 5 Ï c 2 1 b w 2 w Thus, MB 5 MC 5 MA , and M is equidistant from the vertices. 9. Given: n ABC Prove: n ABC is isosceles. Proof: Use the Distance Formula to find AB and BC . AB 5 Ï (2 2 0 w ) 2 1 (8 w 2 0) 2 w 5 Ï 4 1 64 w or Ï 68 w BC 5 Ï (4 2 2 w ) 2 1 (0 w 2 8) 2 w 5 Ï 4 1 64 w or Ï 68 w Since AB 5 BC , A w B w > B w C w .Since the legs are congruent, n ABC is isosceles. Pages 224–226 Practice and Apply 10. • Use the origin as vertex Q of the triangle. • Place the base of the triangle along the positive
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This note was uploaded on 12/19/2011 for the course MAC 1140 taught by Professor Dr.zhan during the Fall '10 term at UNF.

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