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Haven
Senior Member

USA
28 Posts

 Posted - 09/22/2008 :  13:35:48 I am having a problem figuring out a problem in the SAT Study Guide on page 599 problem number 18.The problem states that ABCD is a rectangle and that Points 'A' and 'C' lie on the graph of y = px, where p is a constant. In the problem which is drawn as a graph, point 'A' is located in the third quadrant at (-1/2, A); point 'B' is located in the second quadrant at (-1/2, B); point 'C' is located in the first quadrant at (1/2, C); and point 'D' is located in the fourth quadrant at (-1/2, d ).The problem further states that if the area of ABCD is 4, what is the value of p?I need to know how to find the value of 'p'.I would also like to know what area of mathematics I should look at in order to better understand this type of problem?any help would be greatly appreciated.

Subhotosh Khan

USA
9117 Posts

 Posted - 09/22/2008 :  14:05:06 quote:Originally posted by HavenI am having a problem figuring out a problem in the SAT Study Guide on page 599 problem number 18.The problem states that ABCD is a rectangle and that Points 'A' and 'C' lie on the graph of y = px, where p is a constant. In the problem which is drawn as a graph, point 'A' is located in the third quadrant at (-1/2, A); point 'B' is located in the second quadrant at (-1/2, B); point 'C' is located in the first quadrant at (1/2, C); and point 'D' is located in the fourth quadrant at (-1/2, d ). <<< How is this x co-ordinate negative - in fourth quadrant the x co-ordinates should be positive.The problem further states that if the area of ABCD is 4, what is the value of p?I need to know how to find the value of 'p'.I would also like to know what area of mathematics I should look at in order to better understand this type of problem?any help would be greatly appreciated.

Haven
Senior Member

USA
28 Posts

 Posted - 09/22/2008 :  19:35:33 I stand corrected, the x coordinate in the "D" quadrant should be positive 1/2.Thanks,Haven Williams

Subhotosh Khan

USA
9117 Posts

 Posted - 09/23/2008 :  07:18:12 Now about the problem.Since it is a rectangle (and pair of vertices have same x-coordinate)A = DandB = C......................................(1)ThenAB = B - A andAD = 1Area = 4 = 1*(B - A) ........................(2)using (1) in (2)C - A = 4....................................(3) A & C lie on y = px^3soA = -p/8......................................(4)andC = p/8.......................................(5)Use (3), (4) & (5) to solve for 'p'.

Haven
Senior Member

USA
28 Posts

 Posted - 09/23/2008 :  13:30:17 Thank You Very Much Subhotosh Khan.
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