{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:10:38+00:00","modifiedTime":"2016-03-26T07:10:38+00:00","timestamp":"2022-09-14T17:46:06+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":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"The Euler Line — Practice Geometry Questions","strippedTitle":"the euler line — practice geometry questions","slug":"the-euler-line-practice-geometry-questions","canonicalUrl":"","seo":{"metaDescription":"In geometry, the Euler line is a serious multi-tasker: it contains the centroid, circumcenter, and orthocenter of a triangle. If you know any two of these point","noIndex":0,"noFollow":0},"content":"<p>In geometry, the <i>Euler line</i> is a serious multi-tasker: it contains the centroid, circumcenter, and orthocenter of a triangle. If you know any two of these points, you can determine the Euler line. </p>\n<p>The following practice questions ask you, first, to use the equation for the Euler line to find the <i>y</i>-coordinate for the circumcenter of a triangle, and second, to find the equation for the Euler line given the triangle's centroid and orthocenter.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">The equation for the Euler line of a triangle is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501371.image0.png\" height=\"40\" alt=\"image0.png\" width=\"75\"/>\n<p class=\"child-para\">If the <i>x</i> coordinate of the circumcenter is 5, what is the <i>y</i> coordinate for the circumcenter?</p>\n </li>\n <li><p class=\"first-para\">The centroid of a triangle is (6, 2), and the orthocenter of the triangle is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501372.image1.png\" height=\"45\" alt=\"image1.png\" width=\"59\"/>\n<p class=\"child-para\">What is the equation of the Euler line for this triangle?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">2.75</p>\n<p class=\"child-para\">The circumcenter is on the Euler line. Find the <i>y</i> value by plugging <i>x</i> into the equation of the Euler line:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501373.image2.png\" height=\"40\" alt=\"image2.png\" width=\"121\"/>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501374.image3.png\" height=\"40\" alt=\"image3.png\" width=\"79\"/>\n<p class=\"child-para\">The <i>Euler line</i> is the line that contains the centroid, circumcenter, and orthocenter of a triangle. To find the equation of the line, you first need to determine the slope of the line that contains the two given points:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501375.image4.png\" height=\"77\" alt=\"image4.png\" width=\"157\"/>\n<p class=\"child-para\">Then use the point-slope formula to find the equation of the line:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501376.image5.png\" height=\"157\" alt=\"image5.png\" width=\"117\"/>\n </li>\n</ol>","description":"<p>In geometry, the <i>Euler line</i> is a serious multi-tasker: it contains the centroid, circumcenter, and orthocenter of a triangle. If you know any two of these points, you can determine the Euler line. </p>\n<p>The following practice questions ask you, first, to use the equation for the Euler line to find the <i>y</i>-coordinate for the circumcenter of a triangle, and second, to find the equation for the Euler line given the triangle's centroid and orthocenter.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">The equation for the Euler line of a triangle is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501371.image0.png\" height=\"40\" alt=\"image0.png\" width=\"75\"/>\n<p class=\"child-para\">If the <i>x</i> coordinate of the circumcenter is 5, what is the <i>y</i> coordinate for the circumcenter?</p>\n </li>\n <li><p class=\"first-para\">The centroid of a triangle is (6, 2), and the orthocenter of the triangle is </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501372.image1.png\" height=\"45\" alt=\"image1.png\" width=\"59\"/>\n<p class=\"child-para\">What is the equation of the Euler line for this triangle?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">2.75</p>\n<p class=\"child-para\">The circumcenter is on the Euler line. Find the <i>y</i> value by plugging <i>x</i> into the equation of the Euler line:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501373.image2.png\" height=\"40\" alt=\"image2.png\" width=\"121\"/>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501374.image3.png\" height=\"40\" alt=\"image3.png\" width=\"79\"/>\n<p class=\"child-para\">The <i>Euler line</i> is the line that contains the centroid, circumcenter, and orthocenter of a triangle. To find the equation of the line, you first need to determine the slope of the line that contains the two given points:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501375.image4.png\" height=\"77\" alt=\"image4.png\" width=\"157\"/>\n<p class=\"child-para\">Then use the point-slope formula to find the equation of the line:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501376.image5.png\" height=\"157\" alt=\"image5.png\" width=\"117\"/>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8987"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":207513,"title":"Geometry: 1001 Practice Problems For Dummies Cheat Sheet","slug":"1001-geometry-practice-problems-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207513"}},{"articleId":144555,"title":"Circle Basics for Geometry Problems","slug":"circle-basics-for-geometry-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144555"}},{"articleId":144556,"title":"Coordinate Geometry Formulas","slug":"coordinate-geometry-formulas","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144556"}},{"articleId":144557,"title":"Geometry Practice Problems with Triangles and Polygons","slug":"geometry-practice-problems-with-triangles-and-polygons","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144557"}},{"articleId":143448,"title":"Formulas for Geometric Solids Problems","slug":"formulas-for-geometric-solids-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/143448"}}],"fromCategory":[{"articleId":230077,"title":"How to Copy an Angle Using a Compass","slug":"copy-angle-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230077"}},{"articleId":230072,"title":"How to Copy a Line Segment Using a Compass","slug":"copy-line-segment-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230072"}},{"articleId":230069,"title":"How to Find the Right Angle to Two Points","slug":"find-right-angle-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230069"}},{"articleId":230066,"title":"Find the Locus of Points Equidistant from Two Points","slug":"find-locus-points-equidistant-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230066"}},{"articleId":230063,"title":"How to Solve a Two-Dimensional Locus Problem","slug":"solve-two-dimensional-locus-problem","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230063"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281917,"slug":"geometry-1001-practice-problems-for-dummies-free-online-practice","isbn":"9781118853269","categoryList":["academics-the-arts","math","geometry"],"amazon":{"default":"https://www.amazon.com/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118853261/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/1118853261-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/geometry-1001-practice-problems-for-dummies-cover-9781118853269-193x255.jpg","width":193,"height":255},"title":"Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8986\">Allen Ma</b> and <b data-author-id=\"8987\">Amber Kuang</b> are math teachers at John F. 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The Euler Line — Practice Geometry Questions

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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In geometry, the Euler line is a serious multi-tasker: it contains the centroid, circumcenter, and orthocenter of a triangle. If you know any two of these points, you can determine the Euler line.

The following practice questions ask you, first, to use the equation for the Euler line to find the y-coordinate for the circumcenter of a triangle, and second, to find the equation for the Euler line given the triangle's centroid and orthocenter.

Practice questions

The equation for the Euler line of a triangle is

If the x coordinate of the circumcenter is 5, what is the y coordinate for the circumcenter?
The centroid of a triangle is (6, 2), and the orthocenter of the triangle is

What is the equation of the Euler line for this triangle?

Answers and explanations

2.75

The circumcenter is on the Euler line. Find the y value by plugging x into the equation of the Euler line:
The Euler line is the line that contains the centroid, circumcenter, and orthocenter of a triangle. To find the equation of the line, you first need to determine the slope of the line that contains the two given points:

Then use the point-slope formula to find the equation of the line:

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

This article can be found in the category:

Geometry ,