GRE Quant Ep 3: Coordinate Geometry
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- Опубликовано: 16 июл 2024
- Do you mix up between parallel and perpendicular lines? Do you understand the basics of midpoints, slopes, intercepts, and distance formulas, but still somehow struggle with GRE coordinate geometry during the actual exam?
In this video, Harry -- a GMAT Ninja tutor -- will show you how to think about GRE coordinate geometry. He'll help you understand the content and how to apply the necessary formulas and processes to a GRE coordinate geometry question effectively and efficiently.
This is video #3 in our series of full-length GRE quant lessons. For updates on upcoming videos, please subscribe!
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Chapters:
00:00 Introduction
02:20 Question 1 - Horizontal & Vertical Lines
11:09 Question 2 - Midpoints & the Distance Between Points
21:54 Question 3 - Slopes, Intercepts & Equations of Lines
31:17 Question 4 - Slopes & Intercepts Part II
38:22 Question 5 - Parallel & Perpendicular Lines
45:10 Question 6 - Problem Solving in Coordinate Geometry
53:11 Question 7 - Comparing coordinates
59:49 Question 8 - Find the y-intercept
Thank you so much. Compared to the GMAT questions, the difficult level seems considerably easier. It would be great if you do a video covering: mixture, distance, and work word problems. Thanks!
Thank you for these videos!! For question 4, wouldn't you want to double check that the point of intersection between the two lines corresponds with the graph? For example an answer choice that had a point of intersection with a positive x value would not work even if the slopes and intercepts aligned (in this case both B and D still work). Is this something we should look out for or is there a way to confirm this without doing the additional algebra?
Hi Leah,
You're welcome! I'm so pleased you like the videos. For question 4, if you know that the slope of line P is greater than the slope of line Q and you know the y-intercept of line P is greater than the y-intercept of line Q, it's not possible for the point of intersection to have a positive x-value.
The one other thing you might check is the x-intercept of both lines. From the diagram, we want the x-intercept of line P to be greater (further to the right on the x-axis) than the x-intercept of line Q. If we said the equation of line P was y = ax + b in the same way we did in the video, then we can find the x-intercept by setting y = 0 and solving for x. This gives x = -b/a.
If we consider answer choice (B), line P has a slope of 2 and a y-intercept of 6. By plugging these values into x = -b/a we get x = -6/2 = -3. Doing the same thing for line Q, we get an x-intercept of -4. Since the x-intercept of line P is greater than the x-intercept of line Q, combined with the fact we know the slope and y-intercept of line P are greater than those of line Q, we know the intercept must be in the top-left quadrant. You could follow the same process for answer choice (D) to confirm that one is correct too.
I hope that helps!
@@GRENinjaTutoring I think he meant depending on which quadrant both lines intercept, x intercepts change. Here in the given graph, they are intersecting in 2nd quadrant, but if there intersect in 3rd quadrant, we'd have no answer among the options.
@@user-qz1dg3gh7d , you're absolutely right that if we were given a different graph that had the two lines intersect in the third quadrant then we'd have no answer among the options. However, the graph provided in the question is the one thing we know to be correct as that's the information that was provided in the question.
To know that the two graphs intersect in the second quadrant, it's sufficient to know the slope of P is greater than the slope of Q, the y-intercepts of both P and Q are positive and that of P is greater than that of Q, and the x-intercepts of both P and Q are negative and that of P is greater than that of Q. Since both (B) and (D) satisfy these conditions, we know the lines referred to in these answer choices will intercept in quadrant 2.
We could check this to confirm it if we wanted to, but it's not necessary to do this work to get the correct answer to this question.
I hope that helps!
straight line with linear equartion y=ax+b doenst cross the x line only if the slope m=0
distance racine((x1-x2)**2+(y1-y2)**2) and midpoint ((x1+x2)/2,(y1+y2)/2) formulat in x,y space
at the x intercept y=0
the interecept of a function is where x=0
Dont forget to select two anwers if "all that apply" is specified
Two lonear graphs are perpondicular if the product of the their slopes =-1
Two linear graphs are paralllel the the two slops are equal
You can test points values if you have a qustion about a graph that you vant figure out
Are this question gre level?
Hi there, the questions in this video were designed to cover a range of difficulties. The first five questions will probably give you everything you need to answer coordinate geometry questions up to a 160 level. The final three questions were designed to show you the kind of things the GRE could do to make coordinate geometry questions a bit more difficult. These questions would roughly fall into the 160-165 level.
I hope that helps!