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GMAT Coordinate Geometry
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Author:  questioner [ Sun Aug 22, 2010 1:19 pm ]
Post subject:  GMAT Coordinate Geometry

The two lines y = x and x = -4 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis?
A. √(46)/3
B. 4√2
C. 8
D. 8√2
E. 16

(C) The lines intersect at the point (-4, -4) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height:
A = (1/2) × bh = (1/2) × (4 × 4) = 8
So the area is 8. The correct answer is C.
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Hi, is there a pictorial representation of the triangle that is formed from the above equation?

Thanks.

Author:  Gennadiy [ Sun Aug 22, 2010 1:30 pm ]
Post subject:  Re: GMAT Coordinate Geometry

Here it is:

Image

Triangle ABC is the right triangle (angle ABC = 90 degrees).
AB = 4
BC = 4

Attachments:
triangleABC.gif [5.46 KiB]
Not downloaded yet

Author:  questioner [ Tue Nov 09, 2010 5:22 pm ]
Post subject:  Re: GMAT Coordinate Geometry

Hello,

Based on the information in the stem, to me, the figure that is formed is a square and not a triangle. Since x = -4 forms a straight line parallel to the x-axis and y = x, which translates to y = -4 forms a straight line parallel to the y axis. They both meet at the coordinate (-4.-4), but again, using the x-axis, x = -4 and y = -4 the shape is that of a square not a triangle. Am I missing something?

Author:  Gennadiy [ Tue Nov 09, 2010 5:35 pm ]
Post subject:  Re: GMAT Coordinate Geometry

THE PROPER PICTURE for the question is posted above in this topic.

Note, that the line x = -4 is parallel to the y-axis and crosses the x-axis at the point (-4, 0).

The line y = x and the line y = -4 are different lines. These two lines cross at the point (-4, -4), which happens to be the crossing point of the lines y = x and x = -4 as well.

The following picture demonstrates that the lines y = x and y = -4 are different:

Image
THE PROPER PICTURE for the question is posted above in this topic.

Attachments:
the_lines_-x_equals_y_and_y_equals_-4.gif [4.91 KiB]
Not downloaded yet

Author:  questioner [ Wed Jan 12, 2011 5:39 pm ]
Post subject:  Re: GMAT Coordinate Geometry

Thank you very much!

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