Pre-Calculus Homework Solutions 229

Pre-Calculus Homework Solutions 229 - 57. y 4 ¬ 4x 8 y ¬...

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Unformatted text preview: 57. y 4 ¬ 4x 8 y ¬ 4x 12 Solve a system of equations to find the point of intersection of the medians. x 8 ¬ 4x 12 3x 8 ¬12 3x ¬4 x ¬4 3 y Z(0 , 1 2 ) Y( 4 , 8 ) X(8 , 0 ) x Replace x with 4 in one of the equations to find 3 the y-coordinate. Find an equation of the altitude from X to YZ. The slope of YZ is 012 ( 8 or 1, so the slope of 4) the altitude is 1. y y1 ¬m(x x1) y 0 ¬ 1(x 8) y ¬x 8 Find an equation of the altitude from Z to XY. 80 The slope of XY is 4 8 or 2 , so the slope of 3 4 3 20 3 y y 8 The coordinates of the centroid are 4 , 20 or 33 about (1.3, 6.7). 59. y Z(0 , 1 2 ) the altitude is 3 . 2 y y1 x1) 12 ¬ 3 (x 2 ¬3 x 2 0) 8 ¬3 x 2 12 8 y ¬m(x ¬5 x 2 ¬5x 2 12 Y( 4 , 8 ) y 12 Solve a system of equations to find the point of intersection of the altitudes. x 4 X(8 , 0 ) x Find an equation of the perpendicular bisector of YZ. 4 0 8 12 The midpoint of YZ is or ( 2, 10). 2, 2 The slope of YZ is 012 ( 8 or 1, so the slope of 4) the perpendicular bisector is 1. y y1 m(x x1) y 10 1[x ( 2)] y 10 x2 y x8 Find an equation of the perpendicular bisector of XY. ( The midpoint of XY is 8 2 4) , 0 2 8 or (2, 4). 8 5 ¬x Replace x with 8 in one of the equations to find 5 the y-coordinate. 8 y 8 5 y 48 5 The coordinates of the orthocenter are ( 1.6, 9.6). 58. 8 48 5 , 5 or 2 3 , so the slope of 3 the perpendicular bisector is 2 . Z(0 , 1 2 ) y y1 y Y( 4 , 8 ) m(x x1) 4 3 2 (x 3 2x 3 2x 2) y Find an equation of the median from X to YZ. 4 0 8 12 The midpoint of YZ is or ( 2, 10). 2 2, x 8¬ 8¬ Then the slope of the median is 10 0 or 1. 28 y y1 ¬m(x x1) y 0 ¬ 1(x 8) y ¬x 8 Find an equation of the median from Z to XY. 7¬ 14 5¬ 4 3 2x 5 2x 5 2x 1 1 x Replace x with 14 in one of the equations to find 5 the y-coordinate. 14 y 8 5 ( 4) 0 8 ,2 or (2, 4). 2 Then the slope of the median is 4 12 or 4. 20 The midpoint of XY is 8 y1 4 3 y 1 Solve a system of equations to find the point of intersection of the perpendicular bisectors. X(8 , 0 ) x y y 80 4 8 or The slope of XY is y y 26 5 The coordinates of the circumcenter are 14 , 26 55 or (2.8, 5.2). ¬m(x x1) ¬ 4 (x 2) 231 Chapter 7 ...
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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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