• Board contributors include instructors with "800" GMAT scores.
  • 95% of posts have replies within 24 hours.
  • Join for discounts with 800score, VeritasPrep and ManhattanGMAT


FAQ  - Register  - Search - Login 

All times are UTC - 7 hours




Post new topic Reply to topic  [ 2 posts ] 
Author Message
 Post subject: GMAT Coordinate Geometry
PostPosted: Mon Apr 29, 2013 9:21 am 
Offline
User avatar

Joined: Tue Apr 13, 2010 8:48 am
Posts: 483
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (2,-2), (2, 6), (15, 2), (15,-4)?
A. 91
B. 95
C. 104
D. 117
E. 182

(A) First, we should make a rough sketch of the figure to determine its general shape. Its left side and right side are parallel, with the left side having a length of 8 and the right side having a length of 6. The distance between these two sides is 13.This figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:

Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.

We can now determine the area of the quadrilateral:

Area = 1/2 × (8 + 6) × 13 = 1/2 × 14 × 13 = 7 × 13 = 91.

The correct answer is choice (A).

Alternate Method (Breaking the figure apart):
Without the formula for the area of a trapezoid, we can still solve the problem. We can draw two horizontal lines through the figure, one at y = 2 and one at y = -2 to divide the trapezoid
into an upper triangle, a rectangle, and a lower triangle.

The upper triangle has an area of (1/2) × 4 × 13 = 26.
The rectangle has an area of 4 × 13 = 52.
The lower triangle has an area of 1/2 × 2 × 13 = 13.

Adding these areas, we get the area for the quadrilateral:
52 + 26 + 13 = 91.

Again, we see that the correct answer is choice (A).
-------------

If the y coordinates are -2 and 6 then the length of the left side is 9 and the right side is 7 (you need to count the 0)!
Area = 1/2 × (9+7) × 13 = 104
(and not 91)


Top
 Profile  
 
 Post subject: Re: GMAT Coordinate Geometry
PostPosted: Mon Apr 29, 2013 9:23 am 
Offline
User avatar

Joined: Fri Apr 09, 2010 2:11 pm
Posts: 459
Image

It may be easier if you break each segment in two.
Segment that connects points (2, -2) and (2, 6) we can break into
(2, 0) - (2, 6) segment, length 6
&
(2, -2) - (2, 0) segment, length 2.

The total length is 8.

The same works for the right side.
Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 2 posts ] 

All times are UTC - 7 hours


Who is online

Users browsing this forum: No registered users and 0 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
Template made by DEVPPL -
phpBB SEO
 
GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.