{"id":5335,"date":"2014-12-08T09:00:28","date_gmt":"2014-12-08T17:00:28","guid":{"rendered":"https:\/\/magoosh.com\/gmat\/?p=5335"},"modified":"2024-06-03T16:45:59","modified_gmt":"2024-06-03T23:45:59","slug":"gmat-practice-problems-on-coordinate-geometry","status":"publish","type":"post","link":"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/","title":{"rendered":"GMAT Practice Problems on Coordinate Geometry"},"content":{"rendered":"

\"ppocg_img1\"<\/a><\/p>\n

1) The line shown passes through the point (A, 30).\u00a0 Which of the following is closest to the value of A?<\/p>\n

    \n\t(A) 58
    \n\t(B) 59
    \n\t(C) 60
    \n\t(D) 61
    \n\t(E) 62\n<\/ol>\n

    2) Line A has a slope of \"-{5\/3}\" and passes through the point (\u20132, 7).\u00a0 What is the x-intercept of Line A?<\/p>\n

    \"ppocg_img2\"<\/a><\/p>\n

    \"ppocg_img3\"<\/a><\/p>\n

    3) Line J passes through the points (\u2013 5, \u2013 1), (2, 2), and (5, Q).\u00a0 What is the value of Q?<\/p>\n

    \"AAA<\/a><\/p>\n

    4) A circle has a center of (1, 2) and passes through (1, \u20133).\u00a0 The circle passes through all of the following EXCEPT:<\/p>\n

      \n\t(A) (\u20134, 2)
      \n\t(B) (\u20133, 5)
      \n\t(C) (0, 6)
      \n\t(D) (4, \u20132)
      \n\t(E) (5, 5)\n<\/ol>\n

      5) Points J<\/strong> (3, 1) and K<\/strong> (\u2013 1, \u2013 3) are two vertices of an isosceles triangle.\u00a0 If L<\/strong> is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?<\/p>\n

        \n\t(A) \u20133
        \n\t(B) \u20134
        \n\t(C) \u20135
        \n\t(D) \u20136
        \n\t(E) \u20137\n<\/ol>\n

        6) A parabola has one x-intercept at (\u2013 4, 0).\u00a0 If the vertex is at (2, 5), find the other x-intercept.<\/p>\n

          \n\t(A) 5
          \n\t(B) 6
          \n\t(C) 7
          \n\t(D) 8
          \n\t(E) 9\n<\/ol>\n

           <\/p>\n

          Coordinate Geometry<\/h2>\n

          The coordinate plane is also known as the x-y plane and the Cartesian plane, so named after its discoverer, Mr. Rene Descartes<\/a> (1596 \u2013 1650), the mathematician & philosopher who also said “I think therefore I am<\/em><\/a>.”\u00a0 Of course, it consists of two perpendicular numbers lines, the x- and y-axis, which define a grid that covers the entire infinite plane.\u00a0\u00a0 Here are some previous blogs on this most remarkable mathematical object, the coordinate plane:<\/p>\n

          1) Quadrants in the x-y plane<\/a><\/p>\n

          2) Lines & Slopes in the x-y plane<\/a><\/p>\n

          3) Midpoints and Parallel & Perpendicular Lines<\/a><\/p>\n

          4) Distance in the x-y plane<\/a><\/p>\n

          5) Special Properties of the line y = x<\/a><\/p>\n

          6) an earlier set of Coordinate Geometry practice questions<\/a><\/p>\n

          7) a set of challenging Coordinate Geometry practice questions<\/a><\/p>\n

          If you get some insights from some of those blogs, you might give the problems above a second look before reading the solutions below.<\/p>\n

          \"ppocg_img5\"<\/a><\/p>\n

           <\/p>\n

          Practice problem explanations<\/h2>\n

          1) The line appears to have a slope of \u00bd and y-intercept of 1, so its equation would be<\/p>\n

          y = 0.5x + 1<\/p>\n

          Plug in A for x and 30 for y.<\/p>\n

          30 = 0.5A + 1<\/p>\n

          29 = 0.5A<\/p>\n

          58 = A<\/p>\n

          Answer = (A)<\/strong><\/p>\n

          2) Think about this visually.\u00a0 A slope of \u2013 5\/3 means, among other things, left 3 spaces, down 5.\u00a0 If the line goes through the point (\u20132, 7), then it must also go through (1, 2), which is must closer to the x-intercept.\u00a0 Let’s think about this in the vicinity of the x-intercept.<\/p>\n

          \"ppocg_img6\"<\/a><\/p>\n

          Obviously, (1, 2) is at a height of 2 above the x-axis.\u00a0 Let b be the distance from (1, 0) to the x-intercept.\u00a0\u00a0 We know \u2013h\/b must equal the slope.<\/p>\n

          \"ppocg_img7\"<\/a><\/p>\n

          Now, we just have to add one to that to get the horizontal distance from the origin.<\/p>\n

          \"ppocg_img8\"<\/a><\/p>\n

          Answer = (B)<\/strong><\/p>\n

          3) Think about this visually.\u00a0 From (\u20135, \u20131) to (2, 2), the line moves right 7 and up 3, so that’s a slope of 3\/7.<\/p>\n

          From the point (2, 2) to the point (5, Q), there’s a horizontal distance of 3, an unknown vertical distance — call it h<\/strong>, so that h = Q \u2013 2, or Q = h + 2.\u00a0 The ratio of this vertical and horizontal distance must equal the slope.<\/p>\n

          \"ppocg_img9\"<\/a><\/p>\n

          That’s h.\u00a0 Now, add 2 to get Q.<\/p>\n

          \"ppocg_img10\"<\/a><\/p>\n

          Answer = (C)<\/strong><\/p>\n

          4) The radius is r = 5.\u00a0 First of all, 5 above the center, the circle goes through (1, 7) on the top, and 5 to the left & right of the center, the circle goes through (\u20134, 2) and (6, 2) on the same horizontal line as the center.\u00a0 That first point is choice (A)<\/strong>.<\/p>\n

          That length of 5 can also be the hypotenuse of a 3-4-5 slope triangle, so starting from the center (1, 2), we could go over \u00b13 and up \u00b14, or over \u00b14 and up \u00b15.\u00a0 This means the circle must go through<\/p>\n

          right 3, up 4 = (4, 6)<\/p>\n

          right 4, up 3 = (5, 5) = option (E)<\/strong><\/p>\n

          right 3, down 4 = (4, \u20132) = option (D)<\/strong><\/p>\n

          right 4, down 3 = (5, \u20131)<\/p>\n

          left 3, up 4 = (\u20132, 6)<\/p>\n

          left 4, up 3 = (\u20133, 5) = option (D)<\/strong><\/p>\n

          left 3, down 4 = (\u20132, \u20132)<\/p>\n

          left 4, down 3 = (\u20133, \u20131)<\/p>\n

          That’s all the points other than option (C)<\/strong>.\u00a0 Notice that (\u20132, 6) and (4, 6) are on the circle, so another point between them, on the same horizontal line, (0, 6), could not be on the circle.<\/p>\n

          \"ppocg_img11\"<\/a><\/p>\n

          Answer = (C)<\/strong><\/p>\n

          5) This one looks like it could involve a very complicated calculation, but there’s a very elegant way to do it.\u00a0 This involves special properties of the line y = \u2013 x<\/a>.\u00a0 Notice that the coordinates of J & K have been switched, x for y and vice versa, and they have the opposite \u00b1 signs.\u00a0 This means that J and K are reflections of each other over the mirror line y = \u2013 x.\u00a0 As is always true of any reflection, every point on the mirror line is equidistant from a point and its reflection.\u00a0\u00a0 Thus, we just need any point on the line y = \u2013 x, for example, (\u20136, 6).<\/p>\n

          Answer = (D)<\/strong><\/p>\n

          6) The line of symmetry of a parabola always passes through the vertex, so the equation of the line of symmetry is the vertical line x = 2.\u00a0 The two x-intercepts are symmetrical around this line.\u00a0 The point (\u2013 4, 0) is six units to the left of the symmetry line, so the other should be six units to right, at (8, 0).<\/p>\n

          \"ppocg_img12\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

          1) The line shown passes through the point (A, 30).\u00a0 Which of the following is closest to the value of A? (A) 58 (B) 59 (C) 60 (D) 61 (E) 62 2) Line A has a slope of and passes through the point (\u20132, 7).\u00a0 What is the x-intercept of Line A? 3) Line J […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[124],"tags":[],"ppma_author":[13209],"class_list":["post-5335","post","type-post","status-publish","format-standard","hentry","category-geometry"],"acf":[],"yoast_head":"\nGMAT Practice Problems on Coordinate Geometry - Magoosh Blog \u2014 GMAT\u00ae Exam<\/title>\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\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GMAT Practice Problems on Coordinate Geometry\" \/>\n<meta property=\"og:description\" content=\"1) The line shown passes through the point (A, 30).\u00a0 Which of the following is closest to the value of A? (A) 58 (B) 59 (C) 60 (D) 61 (E) 62 2) Line A has a slope of and passes through the point (\u20132, 7).\u00a0 What is the x-intercept of Line A? 3) Line J […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\" \/>\n<meta property=\"og:site_name\" content=\"Magoosh Blog \u2014 GMAT\u00ae Exam\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/MagooshGMAT\/\" \/>\n<meta property=\"article:published_time\" content=\"2014-12-08T17:00:28+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-06-03T23:45:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/magoosh.com\/gmat\/files\/2014\/11\/ppocg_img1.png\" \/>\n<meta name=\"author\" content=\"Mike M\u1d9cGarry\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:site\" content=\"@MagooshGMAT\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mike M\u1d9cGarry\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\"},\"author\":{\"name\":\"Mike M\u1d9cGarry\",\"@id\":\"https:\/\/magoosh.com\/gmat\/#\/schema\/person\/320346c205075513344435baf9b0521b\"},\"headline\":\"GMAT Practice Problems on Coordinate Geometry\",\"datePublished\":\"2014-12-08T17:00:28+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\"},\"wordCount\":776,\"commentCount\":6,\"publisher\":{\"@id\":\"https:\/\/magoosh.com\/gmat\/#organization\"},\"articleSection\":[\"GMAT Geometry\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\",\"url\":\"https:\/\/magoosh.com\/gmat\/gmat-practice-problems-on-coordinate-geometry\/\",\"name\":\"GMAT Practice Problems on Coordinate Geometry - 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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.","sameAs":["https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured"],"award":["Magna cum laude from Harvard"],"knowsAbout":["GMAT"],"knowsLanguage":["English"],"jobTitle":"Content Creator","worksFor":"Magoosh","url":"https:\/\/magoosh.com\/gmat\/author\/mikemcgarry\/"}]}},"authors":[{"term_id":13209,"user_id":26,"is_guest":0,"slug":"mikemcgarry","display_name":"Mike M\u1d9cGarry","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/6b06de81592cd77bb46aa560cc59aee179cba4d042835c3529221ea1b344cce0?s=96&d=mm&r=g","user_url":"","last_name":"M\u1d9cGarry","first_name":"Mike","description":"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 <a href=\"https:\/\/gmatclub.com\/blog\/2012\/09\/mike-mcgarrys-gmat-experience\/\" rel=\"noopener noreferrer\">GMAT Club<\/a>. Mike holds an A.B. in Physics (graduating <em>magna cum laude<\/em>) 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 <a href=\"https:\/\/www.youtube.com\/c\/MagooshGMATChannel\/featured\" rel=\"noopener noreferrer\">Youtube <\/a>video explanations and resources like <a href=\"https:\/\/magoosh.com\/gmat\/whats-a-good-gmat-score\/\" rel=\"noopener noreferrer\">What is a Good GMAT Score?<\/a> and the <a href=\"https:\/\/magoosh.com\/gmat\/gmat-diagnostic-test\/\" rel=\"noopener noreferrer\">GMAT Diagnostic Test<\/a>."}],"_links":{"self":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/comments?post=5335"}],"version-history":[{"count":0,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/posts\/5335\/revisions"}],"wp:attachment":[{"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/media?parent=5335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/categories?post=5335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/tags?post=5335"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/magoosh.com\/gmat\/wp-json\/wp\/v2\/ppma_author?post=5335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}