{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-12-08T03:03:09+00:00","modifiedTime":"2016-12-08T03:03:09+00:00","timestamp":"2022-09-14T18:16:41+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":"Construct a Line Perpendicular to Another Line Through a Point","strippedTitle":"construct a line perpendicular to another line through a point","slug":"construct-line-perpendicular-another-line-point","canonicalUrl":"","seo":{"metaDescription":"Say you're taking a geometry test, and one question gives you a line along with a point that is not on that line. You're told to construct a line perpendicular ","noIndex":0,"noFollow":0},"content":"Say you're taking a geometry test, and one question gives you a line along with a point that is not on that line. You're told to construct a line perpendicular to the given line that also passes through the point.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-un2013-Before.gif\"><img class=\"aligncenter wp-image-229654 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-un2013-Before.gif\" alt=\"geometry-perpendicular\" width=\"348\" height=\"73\" /></a>\r\n\r\nCan it be done? Well, yes—but you'll need a compass to make it happen.\r\n\r\nThe following figure will help guide you through a construction.\r\n\r\n[caption id=\"attachment_229618\" align=\"aligncenter\" width=\"450\"]<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2013.gif\"><img class=\"wp-image-229618 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2013.gif\" alt=\"geometry-perpendicular-construct\" width=\"450\" height=\"160\" /></a> Constructing a perpendicular line through a point not on a line.[/caption]\r\n\r\nNow, follow these steps:\r\n<ol>\r\n\t<li><strong>Open your compass to a radius <em>r</em> (<em>r</em> must be greater than the distance from <em>J</em> to line <em>AZ</em>), and construct arc (<em>J</em>, <em>r</em>) intersecting line <em>AZ</em> at <em>K</em> and <em>L.</em></strong></li>\r\n\t<li><strong>Leaving your compass open to radius <em>r</em> (other radii would also work), construct arc (<em>K</em>, <em>r</em>) and arc (<em>L</em>, <em>r</em>)—on the side of line <em>AZ</em> that's opposite point <em>J</em>—intersecting each other at point <em>M.</em></strong></li>\r\n\t<li><strong>Draw line <em>JM,</em> and that's a wrap.</strong></li>\r\n</ol>","description":"Say you're taking a geometry test, and one question gives you a line along with a point that is not on that line. You're told to construct a line perpendicular to the given line that also passes through the point.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-un2013-Before.gif\"><img class=\"aligncenter wp-image-229654 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-un2013-Before.gif\" alt=\"geometry-perpendicular\" width=\"348\" height=\"73\" /></a>\r\n\r\nCan it be done? Well, yes—but you'll need a compass to make it happen.\r\n\r\nThe following figure will help guide you through a construction.\r\n\r\n[caption id=\"attachment_229618\" align=\"aligncenter\" width=\"450\"]<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2013.gif\"><img class=\"wp-image-229618 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2013.gif\" alt=\"geometry-perpendicular-construct\" width=\"450\" height=\"160\" /></a> Constructing a perpendicular line through a point not on a line.[/caption]\r\n\r\nNow, follow these steps:\r\n<ol>\r\n\t<li><strong>Open your compass to a radius <em>r</em> (<em>r</em> must be greater than the distance from <em>J</em> to line <em>AZ</em>), and construct arc (<em>J</em>, <em>r</em>) intersecting line <em>AZ</em> at <em>K</em> and <em>L.</em></strong></li>\r\n\t<li><strong>Leaving your compass open to radius <em>r</em> (other radii would also work), construct arc (<em>K</em>, <em>r</em>) and arc (<em>L</em>, <em>r</em>)—on the side of line <em>AZ</em> that's opposite point <em>J</em>—intersecting each other at point <em>M.</em></strong></li>\r\n\t<li><strong>Draw line <em>JM,</em> and that's a wrap.</strong></li>\r\n</ol>","blurb":"","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> has taught pre-algebra through calculus for more than 25 years. 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Construct a Line Perpendicular to Another Line Through a Point

By: Mark Ryan and

Updated: 12-08-2016

From The Book: Geometry For Dummies

Geometry For Dummies

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Say you're taking a geometry test, and one question gives you a line along with a point that is not on that line. You're told to construct a line perpendicular to the given line that also passes through the point.

Can it be done? Well, yes—but you'll need a compass to make it happen.

The following figure will help guide you through a construction.

Constructing a perpendicular line through a point not on a line.

Now, follow these steps:

Open your compass to a radius r (r must be greater than the distance from J to line AZ), and construct arc (J, r) intersecting line AZ at K and L.
Leaving your compass open to radius r (other radii would also work), construct arc (K, r) and arc (L, r)—on the side of line AZ that's opposite point J—intersecting each other at point M.
Draw line JM, and that's a wrap.

About This Article

This article is from the book:

Geometry For Dummies ,

About the book author:

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

This article can be found in the category:

Geometry ,

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