Pre-Calculus Homework Solutions 75

# Pre-Calculus Homework Solutions 75 - 3 4x 23 2x y 4 y 2x 4...

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23. 2 x y ¬ 4 y ¬ 2 x 4 y ¬ 2 x 4 First, write an equation of a line p perpendicular to the lines y 2 x 3 and y 2 x 4. The slope of p is the opposite reciprocal of 2, or 1 2 . Use the y -intercept of the line y 2 x 3, (0, 3), as one of the endpoints of the perpendicular segment. y y 1 ¬ m ( x x 1 ) y ( 3) ¬ 1 2 ( x 0) y 3 ¬ 1 2 x y ¬ 1 2 x 3 Next, use a system of equations to determine the point of intersection of the line y 2 x 4 and p. 2 x 4 ¬ 1 2 x 3 2 x 1 2 x ¬ 3 4 5 2 x ¬ 7 x ¬ 1 5 4 y ¬ 2 1 5 4 4 y ¬ 8 5 The point of intersection is 1 5 4 , 8 5 . Then, use the Distance Formula to determine the distance between (0, 3) and 1 5 4 , 8 5 . d ¬ ( x 2 x 1 ) 2 ( y 2 y 1 ) 2 ¬ 1 5 4 0 2 8 5 ( 3) 2 ¬ 1 5 4 2 7 5 2 ¬ 1 2 9 5 6 4 2 9 5 ¬ 2 2 4 5 5 or 9.8 The distance between the lines is 9.8 units. 24. 3 x 4 y ¬ 20 4 y ¬ 3 x 20 y ¬ 3 4 x 5 First, write an equation of a line p perpendicular to the lines y 3 4 x 1 and y 3 4 x 5. The slope of p is the opposite reciprocal of 3 4 , or 4 3 .
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