Coordinate Plane - triangle

This topic has 4 expert replies and 1 member reply
szDave Senior | Next Rank: 100 Posts Default Avatar
27 Oct 2012
44 messages
Followed by:
1 members

Coordinate Plane - triangle

Post Mon Jan 21, 2013 10:52 am
Elapsed Time: 00:00
    I calculated the rectangulars area and subtracted the area of 3 perpendicular triangle, and got 8, but this is the wrong answer.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Mon Jan 21, 2013 11:13 am
    Sure, 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:

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

    Answer = A


    Brent Hanneson – Founder of
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

    GMAT/MBA Expert

    Anurag@Gurome GMAT Instructor
    02 Apr 2010
    3835 messages
    Followed by:
    516 members
    1848 times
    GMAT Score:
    Post Mon Jan 21, 2013 7:36 pm
    szDave wrote:
    I calculated the rectangulars area and subtracted the area of 3 perpendicular triangle, and got 8, but this is the wrong answer.

    Here's one more approach, other than the one already explained by Brent.

    Formula for finding area of a triangle in a coordinate system = (1/2){(x1 - x2).(y2 - y3) - (y1 - y2).(x2 - x3)}

    In the given question, area of triangle = 1/2 {(-3)(1) - (-4).(7)} = 12.5 sq units

    The correct answer is A.

    Anurag Mairal, Ph.D., MBA
    GMAT Expert, Admissions and Career Guidance
    Gurome, Inc.
    1-800-566-4043 (USA)

    Join Our Facebook Groups
    GMAT with Gurome
    Admissions with Gurome
    Career Advising with Gurome

    Post Tue Jan 22, 2013 7:25 am
    Here's an easier way to approach the problem: generally speaking, when the GMAT asks you to find areas of triangles in a coordinate plane, it's going to be an easy triangle to calculate. This almost always means a RIGHT TRIANGLE (or perhaps an equilateral that we can split into right triangles).

    Can we figure out if this is a right triangle? It looks like it. To know for sure, though, we'd have to prove that two of the sides are perpendicular. To do that, we need to calculate the slopes (vertical change/horizontal change, or rise/run)

    The side from Q to P has a slope of -3/4 (a rise of -3, a run of 4).
    The side from P to R has a slope of 4/3 (a rise of 4, a run of 3)

    The slopes are negative reciprocals, so the lines are perpendicular. It's a RIGHT TRIANGLE! Now all we have to do is figure out the length of sides QP and PR. It's probably not going to be hard to calculate these lengths - they are almost always "special" right triangles.

    To find QP, imagine that it's the hypotenuse of the triangle formed by the x and y axes. One side has a length of 3, the other is 4, so the hypotenuse - QP - must be 5.

    To find PR, draw an imaginary line down to the x axis, forming another triangle. It's a 3-4-5 triangle again!

    Both QP and PR have a length of 5, so we take (1/2)(base * height):

    (1/2)(5*5) = 12.5

    The answer is A.


    Ceilidh Erickson
    Manhattan Prep GMAT & GRE instructor
    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education

    Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience.
    Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry!

    Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week.
    Post Tue Jan 22, 2013 8:05 am
    In the rectangular coordinate system below, the are of triangular region PQR is


    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.

    Mitch Hunt
    GMAT Private Tutor
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at

    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    szDave Senior | Next Rank: 100 Posts Default Avatar
    27 Oct 2012
    44 messages
    Followed by:
    1 members
    Post Wed Jan 23, 2013 3:06 am
    I am impressed by you! 4 ways to solve it! Smile

    Best Conversation Starters

    1 AbeNeedsAnswers 44 topics
    2 amontobin 16 topics
    3 jjjinapinch 13 topics
    4 richachampion 11 topics
    5 NandishSS 9 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Matt@VeritasPrep

    Veritas Prep

    82 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    76 posts
    3 image description Rich.C@EMPOWERgma...


    73 posts
    4 image description DavidG@VeritasPrep

    Veritas Prep

    67 posts
    5 image description Jay@ManhattanReview

    Manhattan Review

    66 posts
    See More Top Beat The GMAT Experts