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Haven
Senior Member

USA
28 Posts

Posted - 09/22/2008 :  13:35:48  Show Profile  Reply with Quote
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
9117 Posts

Posted - 09/22/2008 :  14:05:06  Show Profile  Reply with Quote
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  Show Profile  Reply with Quote
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
9117 Posts

Posted - 09/23/2008 :  07:18:12  Show Profile  Reply with Quote
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  Show Profile  Reply with Quote
Thank You Very Much Subhotosh Khan.
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