Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

coordinate geometry

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16206
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Dec 05, 2014 5:39 pm
chacha0212 wrote:Image
Let's draw a rectangle around the triangle (as shown below) and then subtract from the rectangle's area (28), the areas of the 3 right triangles that surround the triangle in question.

We get the following:
Image

So, the area of PQR = 28 - (3.5 + 6 + 6) = 12.5

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Sat Dec 06, 2014 4:35 am
In the rectangular coordinate system below, the are of triangular region PQR is

12.5
14
10√2
16
25
Image

The area of the rectangle drawn around triangle PQR = 7*4 = 28.
Since triangle PQR takes up less than half the rectangle, PQR < 14.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members
Thanked: 1443 times

by ceilidh.erickson » Tue Dec 09, 2014 8:35 am
Brent and Mitch's explanations are both great approaches, but I just wanted to extrapolate a more general rule from this... in geometry, especially in area problems, the GMAT will often give you shapes that are difficult (or even impossible) to calculate on their own. In these cases, it's most helpful to think in terms of NEGATIVE SPACE: calculate the area of a larger shape that's easier to find, then subtract away the pieces that you don't want, leaving the area of the shape that you're trying to find.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top
Join the discussion
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Fri Dec 19, 2014 6:32 am
In this example, we can see that to travel from Q to P, we go [4,-3]
and to go from P to R, we go [3,4]
Hence line QP is perpendicular to PR.
In other words, QPR is a right-angle triangle.
Using 3-4-5, we also see that QP = PR = 5
So the area is simply 5x5/2 = 12.5
Top
Join the discussion
GMAT Instructor
Posts: 2629
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Mon Dec 22, 2014 12:52 pm
One last cool note about this problem. Suppose we have the triangle as shown below.

Image

Since each of the other triangles is a 3-4-5, each other triangle must have angles of a and b, whatever those are. We know that a + b = 90, and we also know that 180 - (a+b) = the third angle of the blue triangle, since a, b, and that third angle are on a line.

Hence the blue triangle is a right triangle, since 180-(a+b) = 90°. That means that it has a base of 5 and a height of 5, and its area = 5*5/2 = 12.5.
Top
Join the discussion