{"id":9090,"date":"2012-05-25T09:00:22","date_gmt":"2012-05-25T16:00:22","guid":{"rendered":"https:\/\/magoosh.com\/gre\/?p=9090"},"modified":"2017-05-29T00:58:48","modified_gmt":"2017-05-29T07:58:48","slug":"gre-coordinate-geometry-shortcut-no-graphs","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/","title":{"rendered":"GRE Coordinate Geometry Shortcut: No Graphs!"},"content":{"rendered":"

For many, coordinate geometry is already a daunting concept. When a question dispenses with the graph all together, students can feel even more at a loss. If you fall into this group, do not despair. Here is a helpful guideline:<\/p>\n

 <\/p>\n

Do Not Always Draw the Graph<\/h2>\n

This advice may seem counterintuitive. After all, the problem didn\u2019t provide a graph. Wouldn\u2019t the first step be to graph the problem out?<\/p>\n

Many coordinate geometry concepts sans graph are testing your conceptual thinking. Take the follow problem:<\/p>\n

1. Which of the following lines do not contain coordinate points that are both negative?<\/p>\n

    \n
  1. \"y<\/li>\n
  2. \"3y<\/li>\n
  3. \"x<\/li>\n
  4. \"3y<\/li>\n
  5. \"x<\/li>\n<\/ol>\n

     <\/p>\n

    Solution:<\/strong><\/p>\n

    The slope formula is important \u2013 if the question is explicitly asking for the slope. What is often more important is knowing that a line with a negative slope \u2013 from left to right \u2013 slopes downward. A positive slope, unsurprisingly, slopes upward.<\/p>\n

    Think of it this way \u2013 start at a negative x-coordinate (say -2) of a line. If you were to place a ball on the line would roll down the line as it moved into positive territory for the x-coordinate? If so the line is negative, if not the line is positive.<\/p>\n

    For this problem, we are looking for a line that does not pass through the third quadrant \u2013 the quadrant in which x and y are both negative. Graph the point (-2, -2). That\u2019s in the third quadrant.<\/p>\n

    Now here\u2019s the big conceptual part \u2013 any line that slopes upwards will always pass through Quadrant III. Graph it if you have to \u2013 or simply imagine a line of infinite length sloping upwards. Anyway you try to do so there will always be the Third Quadrant waiting to claim a part of your line.<\/p>\n

    Now, imagine a downward sloping line. Is it also crossing through the third quadrant? Well, move the entire line to the right. At a certain point, your line will no longer be in the Third Quadrant. As long as that line crosses the y-axis at a positive value, it will never cross through the Third Quadrant.<\/p>\n

    Now you only need to find two things: a line that has a positive y-intercept and a negative slope. And that is much better than having to graph every one of the equations in answer choices A \u2013 E!<\/p>\n

    Only answer (C) x + y = 2, which can be re-written as y = -x + 2, has a negative slope (-1) and positive y-intercept (+2).<\/p>\n

     <\/p>\n

    Takeaway<\/h2>\n

    If a coordinate geometry question does not provide a graph, it is often testing conceptual thinking. So unless you are really desperate (which can happen on the GRE), and have time to spare, avoid graphing and think conceptually.<\/p>\n

    If you are unsure what to do, take a step back from the problem and ask yourself: will graphing this problem out take a long time? If the answer is yes, then there is very likely a much faster, no-graph approach.<\/p>\n

     <\/p>\n","protected":false},"excerpt":{"rendered":"

    For many, coordinate geometry is already a daunting concept. When a question dispenses with the graph all together, students can feel even more at a loss. If you fall into this group, do not despair. Here is a helpful guideline:   Do Not Always Draw the Graph This advice may seem counterintuitive. After all, the […]<\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[42,25],"tags":[],"ppma_author":[12264],"class_list":["post-9090","post","type-post","status-publish","format-standard","hentry","category-geometry","category-math"],"acf":[],"yoast_head":"\nGRE Coordinate Geometry Shortcut: No Graphs! - Magoosh Blog \u2014 GRE\u00ae Test<\/title>\n<meta name=\"description\" content=\"Check out this helpful guideline to the GRE Coordinate Geometry and find out why you should avoid graphs and start thinking conceptually!\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GRE Coordinate Geometry Shortcut: No Graphs!\" \/>\n<meta property=\"og:description\" content=\"Check out this helpful guideline to the GRE Coordinate Geometry and find out why you should avoid graphs and start thinking conceptually!\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GRE\u00ae Test\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Magoosh\/\" \/>\n<meta property=\"article:author\" content=\"https:\/\/www.facebook.com\/ChrisLeleMagoosh1\/\" \/>\n<meta property=\"article:published_time\" content=\"2012-05-25T16:00:22+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2017-05-29T07:58:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gre\/files\/2016\/09\/Magoosh-Facebook-Default-Pic.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Chris Lele\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@chrismagoosh\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGRE\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Chris Lele\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\"},\"author\":{\"name\":\"Chris Lele\",\"@id\":\"https:\/\/magoosh.com\/gre\/#\/schema\/person\/3b6630b4f786513b81a860849cffd546\"},\"headline\":\"GRE Coordinate Geometry Shortcut: No Graphs!\",\"datePublished\":\"2012-05-25T16:00:22+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\"},\"wordCount\":512,\"commentCount\":36,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gre\/#organization\"},\"articleSection\":[\"GRE Geometry\",\"GRE Math\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\",\"url\":\"https:\/\/magoosh.com\/gre\/gre-coordinate-geometry-shortcut-no-graphs\/\",\"name\":\"GRE Coordinate Geometry Shortcut: No Graphs! 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