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Haven
Senior Member
USA
28 Posts |
 Posted - 09/22/2008 : 13:35:48
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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.
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Subhotosh Khan
Advanced Member
USA
9114 Posts |
Posted - 09/22/2008 : 14:05:06
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quote:
Originally posted by Haven
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 ). <<< 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.
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Haven
Senior Member
USA
28 Posts |
Posted - 09/22/2008 : 19:35:33
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I stand corrected, the x coordinate in the "D" quadrant should be positive 1/2.
Thanks,
Haven Williams
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Subhotosh Khan
Advanced Member
USA
9114 Posts |
Posted - 09/23/2008 : 07:18:12
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Now about the problem.
Since it is a rectangle (and pair of vertices have same x-coordinate)
A = D
and
B = C......................................(1)
Then
AB = B - A and
AD = 1
Area = 4 = 1*(B - A) ........................(2)
using (1) in (2)
C - A = 4....................................(3)
A & C lie on y = px^3
so
A = -p/8......................................(4)
and
C = p/8.......................................(5)
Use (3), (4) & (5) to solve for 'p'.
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Haven
Senior Member
USA
28 Posts |
Posted - 09/23/2008 : 13:30:17
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| Thank You Very Much Subhotosh Khan. |
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Interactive Math Goodies Software
SAT Question #3
