The Pythagorean Theorem on the GMAT

January 4, 2012

There’s a reason this is the most famous theorem in mathematics! This remarkable theorem is one of the most versatile and highly adaptable formulas in existence. Of course, I’m sure you remember that it says: For any right triangle,

Of course, if any question gives you two sides of a right triangle and asks you to find the third, you will use this formula. Here are a couple problems to show its other guises.

Practice Questions: Using the Pythagorean Theorem

1) In the coordinate plane, point A has coordinates (-2, -1) and point B has coordinates (4, 7). What is the length of segment AB?

2) Paul drove 50 miles north, then changed direction and drove 120 miles east. At the end of this trip, how far was he from his starting point?

Answers and Explanations

1) The easiest distances to find in the coordinate plane are the horizontal and vertical lines, so we begin by drawing those.

For the lengths of AC and BC, we can simply count boxes. AC = 6 and BC = 8. These are the two “legs” of a right triangle, and AB is the hypotenuse, so

AB=10

Answer: A.

2) Essentially, Paul drove along the legs of a big right triangle, and the hypotenuse is how far he is from his starting point.

Therefore,

Answer: C.

Author

Mike MᶜGarry

Mike served as a GMAT Expert at Magoosh, helping create hundreds of lesson videos and practice questions to help guide GMAT students to success. He was also featured as “member of the month” for over two years at GMAT Club. Mike holds an A.B. in Physics (graduating magna cum laude) and an M.T.S. in Religions of the World, both from Harvard. Beyond standardized testing, Mike has over 20 years of both private and public high school teaching experience specializing in math and physics. In his free time, Mike likes smashing foosballs into orbit, and despite having no obvious cranial deficiency, he insists on rooting for the NY Mets. Learn more about the GMAT through Mike’s Youtube video explanations and resources like What is a Good GMAT Score? and the GMAT Diagnostic Test.

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Comments

7 responses to “The Pythagorean Theorem on the GMAT”

Rawan Aljallal

June 9, 2018

in the first question, the B stops at 7 not 8, so the answer would be 9.2.
also, the second question I got 10 root 17 as I learned from right triangles video

Reply
1. Magoosh Test Prep Expert
  
  July 4, 2018
  
  Hi Rawan,
  
  I’m not sure if I understand your questions, but I’ll do my best to answer them! In the first question, we are looking for the entire length of B, not just the length above the x-axis. The “y” coordinate is 7, but we must add 1 because the line segment AB dips below the x-axis. 7+1=8, so that is our B value!
  
  Can you tell me how you got 10root17 for the second question? If I see your process, I can tell you where you might have gone wrong 🙂
  
  Reply
Sirisha

December 2, 2014

Hi, In the explanation to problem 1 above, you mentioned to simply count the number of boxes to get AC and BC. In the real GMAT, is the co-ordinate plane given in box style? Thank you.

Reply
1. Mike
  
  December 2, 2014
  
  Dear Sirisha,
  I’m happy to respond. 🙂 Sometimes the GMAT gives the gridlines and sometimes it doesn’t, but even if you are given no diagram at all, it should not be hard to figure out, say, that from the x-coordinate of A, -2, to the x-coordinate of B, 4, there are 6 units. You shouldn’t need the picture at all to be able to count the number of units along a horizontal or vertical line in the coordinate plane.
  Does this make sense?
  Mike 🙂
  
  Reply
  1. John Green
    
    March 21, 2017
    
    If it only gives coordinates of ‘A’ and ‘B’… what’s the best way for me to know that it is indeed a right triangle? I’m visually oriented so sometimes seeing text is hard for me to decipher into a picture into my mind.
    
    Reply
    1. Magoosh Test Prep Expert
      
      March 21, 2017
      
      In many questions, including the second question in this post, you’ll be explicitly told that the triangle is a right triangle. In that case, just look at the angle that clearly looks “right” (visually like the corner of a square), and you’ll have the visual cue that helps you really store that image in your mind.
      
      In the case of the first question, every square in a coordinate plane grid is a set of right angles. (Because, of course, squares have four right angles.) So simply envision the grid boundaries as part of the right triangle, and you’ll be able to visualize your right triangle.
      
      Still in other cases, the problem will tell you that you have a right triangle without using text. Instead, the “right angle” symbol will appear within the triangle figure. This symbol is a little square inside the right angle. To see what this looks like, check out the main image (top, right hand corner) for the Wikipedia article on “right triangle.“
      
      Reply
2. SSY
  
  February 6, 2015
  
  yes, sometimes it does and sometimes it doesnt.
  
  Reply