{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T15:47:52+00:00","modifiedTime":"2016-03-26T15:47:52+00:00","timestamp":"2022-09-14T18:06:08+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"ACT","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"},"slug":"act","categoryId":33775}],"title":"Coordinate Geometry Formulas You Must Know for the ACT","strippedTitle":"coordinate geometry formulas you must know for the act","slug":"coordinate-geometry-formulas-you-must-know-for-the-act","canonicalUrl":"","seo":{"metaDescription":"Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you shoul","noIndex":0,"noFollow":0},"content":"<p>Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you should remember:</p>\n<ul class=\"level-one\">\n <li><p class=\"first-para\"><b>Midpoint formula.</b> The formula for coordinates of the midpoint of a line segment between any two points (<i>x</i><i><sub>1</sub></i>, <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355367.image0.png\" width=\"193\" height=\"48\" alt=\"image0.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Distance formula.</b> The formula for the length of a line segment between any two points (<i>x</i><i><sub>1</sub></i>, <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355368.image1.png\" width=\"235\" height=\"36\" alt=\"image1.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Rise-run slope formula. </b>The formula for the slope of a line in terms of the rise and the run is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355369.image2.png\" width=\"88\" height=\"37\" alt=\"image2.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Two-point slope formula. </b>The formula for the slope of a line that includes the points (<i>x</i><i><sub>1</sub></i><i>,</i> <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355370.image3.png\" width=\"108\" height=\"45\" alt=\"image3.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Axis of symmetry of a parabola. </b>The <i>axis of symmetry</i> is the vertical line that divides a parabola down the middle. For a quadratic function <i>y</i> = <i>ax</i><i><sup>2</sup></i> + <i>bx</i> + <i>c,</i> the formula for the equation of the axis of symmetry is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355371.image4.png\" width=\"59\" height=\"37\" alt=\"image4.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Vertex of a parabola. </b>The <i>vertex</i> of a parabola is the point where the parabola changes directions. It’s always either the lowest or the highest point on the parabola. Here’s the formula for the coordinates of the vertex for the quadratic function <i>y</i> = <i>ax</i><i><sup>2</sup></i><i> </i>+ <i>bx </i>+ <i>c:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355372.image5.png\" width=\"183\" height=\"48\" alt=\"image5.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Formula for graphing a circle.</b> The formula for the equation of a circle of radius <i>r</i> centered at the point (<i>h,</i> <i>k</i>) is:</p>\n<p class=\"child-para\">(<i>x</i> – <i>h</i>)<sup>2</sup> + (<i>y</i> – <i>k</i>)<sup>2</sup> = <i>r</i><sup>2</sup></p>\n </li>\n</ul>","description":"<p>Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you should remember:</p>\n<ul class=\"level-one\">\n <li><p class=\"first-para\"><b>Midpoint formula.</b> The formula for coordinates of the midpoint of a line segment between any two points (<i>x</i><i><sub>1</sub></i>, <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355367.image0.png\" width=\"193\" height=\"48\" alt=\"image0.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Distance formula.</b> The formula for the length of a line segment between any two points (<i>x</i><i><sub>1</sub></i>, <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355368.image1.png\" width=\"235\" height=\"36\" alt=\"image1.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Rise-run slope formula. </b>The formula for the slope of a line in terms of the rise and the run is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355369.image2.png\" width=\"88\" height=\"37\" alt=\"image2.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Two-point slope formula. </b>The formula for the slope of a line that includes the points (<i>x</i><i><sub>1</sub></i><i>,</i> <i>y</i><i><sub>1</sub></i>) and (<i>x</i><i><sub>2</sub></i><i>,</i> <i>y</i><i><sub>2</sub></i>) is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355370.image3.png\" width=\"108\" height=\"45\" alt=\"image3.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Axis of symmetry of a parabola. </b>The <i>axis of symmetry</i> is the vertical line that divides a parabola down the middle. For a quadratic function <i>y</i> = <i>ax</i><i><sup>2</sup></i> + <i>bx</i> + <i>c,</i> the formula for the equation of the axis of symmetry is:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355371.image4.png\" width=\"59\" height=\"37\" alt=\"image4.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Vertex of a parabola. </b>The <i>vertex</i> of a parabola is the point where the parabola changes directions. It’s always either the lowest or the highest point on the parabola. Here’s the formula for the coordinates of the vertex for the quadratic function <i>y</i> = <i>ax</i><i><sup>2</sup></i><i> </i>+ <i>bx </i>+ <i>c:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/355372.image5.png\" width=\"183\" height=\"48\" alt=\"image5.png\"/>\n </li>\n <li><p class=\"first-para\"><b>Formula for graphing a circle.</b> The formula for the equation of a circle of radius <i>r</i> centered at the point (<i>h,</i> <i>k</i>) is:</p>\n<p class=\"child-para\">(<i>x</i> – <i>h</i>)<sup>2</sup> + (<i>y</i> – <i>k</i>)<sup>2</sup> = <i>r</i><sup>2</sup></p>\n </li>\n</ul>","blurb":"","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"primaryCategoryTaxonomy":{"categoryId":33775,"title":"ACT","slug":"act","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33775"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":208624,"title":"ACT Math For Dummies Cheat Sheet","slug":"act-math-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/208624"}},{"articleId":187911,"title":"Solving Math Word Problems on the ACT","slug":"solving-math-word-problems-on-the-act","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187911"}},{"articleId":187910,"title":"Using Charts and Pictures to Answer ACT Math Questions","slug":"using-charts-and-pictures-to-answer-act-math-questions","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187910"}},{"articleId":187907,"title":"Test-Taking Strategies for the Math Portion of the ACT","slug":"test-taking-strategies-for-the-math-portion-of-the-act","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/187907"}},{"articleId":173579,"title":"Practice Mathematics Test 2 for the ACT — 60 Questions","slug":"practice-mathematics-test-2-for-the-act-60-questions","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/173579"}}],"fromCategory":[{"articleId":294142,"title":"ACT Prep 2023 For Dummies Cheat Sheet","slug":"act-prep-2023-for-dummies-cheat-sheet","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/294142"}},{"articleId":268046,"title":"How to Organize Your ACT Essay","slug":"how-to-organize-your-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268046"}},{"articleId":268043,"title":"How to Write a Great ACT Essay","slug":"how-to-write-a-great-act-essay","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268043"}},{"articleId":268033,"title":"ACT Geometry Test: Triangle Trauma","slug":"act-geometry-test-triangle-trauma","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268033"}},{"articleId":268023,"title":"ACT Geometry Test: Analyzing Angles","slug":"act-geometry-test-analyzing-angles","categoryList":["academics-the-arts","study-skills-test-prep","act"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/268023"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281928,"slug":"act-math-for-dummies","isbn":"9781118001547","categoryList":["academics-the-arts","study-skills-test-prep","act"],"amazon":{"default":"https://www.amazon.com/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118001540-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118001540/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/act-math-for-dummies-cover-9781118001547-193x255.jpg","width":193,"height":255},"title":"ACT Math For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"9399\">Mark Zegarelli</b> is the author of <i>Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies</i> (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher. </p>","authors":[{"authorId":9399,"name":"Mark Zegarelli","slug":"mark-zegarelli","description":" <b>Mark Zegarelli</b> is a professional writer with degrees in both English and Math from Rutgers University. He has earned his living for many years writing vast quantities of logic puzzles, a hefty chunk of software documentation, and the occasional book or film review. Along the way, he’s also paid a few bills doing housecleaning, decorative painting, and (for ten hours) retail sales. He likes writing best, though.","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/9399"}}],"_links":{"self":"https://dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","act"]},{"key":"isbn","values":["9781118001547"]}]\" id=\"du-slot-632218101120d\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{"key":"cat","values":["academics-the-arts","study-skills-test-prep","act"]},{"key":"isbn","values":["9781118001547"]}]\" 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Coordinate Geometry Formulas You Must Know for the ACT

By: Mark Zegarelli and

Updated: 03-26-2016

From The Book: ACT Math For Dummies

ACT Math For Dummies

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Some of the questions on the ACT Math test deal with coordinate geometry. When solving coordinate geometry problems, there are several useful formulas you should remember:

Midpoint formula. The formula for coordinates of the midpoint of a line segment between any two points (x₁, y₁) and (x₂, y₂) is:
Distance formula. The formula for the length of a line segment between any two points (x₁, y₁) and (x₂, y₂) is:
Rise-run slope formula. The formula for the slope of a line in terms of the rise and the run is:
Two-point slope formula. The formula for the slope of a line that includes the points (x₁, y₁) and (x₂, y₂) is:
Axis of symmetry of a parabola. The axis of symmetry is the vertical line that divides a parabola down the middle. For a quadratic function y = ax² + bx + c, the formula for the equation of the axis of symmetry is:
Vertex of a parabola. The vertex of a parabola is the point where the parabola changes directions. It’s always either the lowest or the highest point on the parabola. Here’s the formula for the coordinates of the vertex for the quadratic function y = ax² + bx + c:
Formula for graphing a circle. The formula for the equation of a circle of radius r centered at the point (h, k) is:

(x – h)² + (y – k)² = r²

About This Article

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ACT Math For Dummies ,

About the book author:

Mark Zegarelli is the author of Basic Math & Pre-Algebra For Dummies, SAT Math For Dummies (both from Wiley), and five other books on basic math, calculus, and logic. He holds degrees in both English and math from Rutgers University and is a math tutor and teacher.

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