{"id":167244,"date":"2024-11-15T09:02:28","date_gmt":"2024-11-15T09:02:28","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167244"},"modified":"2024-11-15T09:02:31","modified_gmt":"2024-11-15T09:02:31","slug":"three-ballet-dancers-are-position-on-stage","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/three-ballet-dancers-are-position-on-stage\/","title":{"rendered":"Three ballet dancers are position on stage."},"content":{"rendered":"\n<p>Three ballet dancers are position on stage. If Tina is 7 feet straight behind Maria and 6 feet directly left of Shawn, how far is Maria from Shawn? If necessary, round to the nearest tenth.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve this problem, we need to determine the distance between Maria and Shawn based on their positions relative to Tina.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Visualizing the setup<\/h3>\n\n\n\n<p>We can assume a coordinate system where we place the dancers on a flat plane. Tina is described as being 7 feet directly behind Maria and 6 feet directly left of Shawn. We can think of the positions of the dancers as forming a right triangle.<\/p>\n\n\n\n<p>Let\u2019s place Tina at the origin of the coordinate plane, or at point ((0, 0)). From the description:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Tina is 7 feet directly behind Maria. In a coordinate plane, &#8220;behind&#8221; would correspond to moving along the negative y-axis. Therefore, Maria is at ((0, 7)) because she is 7 feet in front of Tina (in the positive y-direction).<\/li>\n\n\n\n<li>Tina is 6 feet directly left of Shawn. Being &#8220;left&#8221; corresponds to moving along the negative x-axis, so Shawn is at ((-6, 0)) since he is 6 feet to the left of Tina.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Applying the distance formula<\/h3>\n\n\n\n<p>Now, we need to calculate the distance between Maria and Shawn. The distance formula in a 2D plane is given by:<\/p>\n\n\n\n<p>[<br>d = \\sqrt{(x_2 &#8211; x_1)^2 + (y_2 &#8211; y_1)^2}<br>]<\/p>\n\n\n\n<p>Where ((x_1, y_1)) is Maria&#8217;s position, and ((x_2, y_2)) is Shawn&#8217;s position. From the coordinates:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Maria: ((0, 7))<\/li>\n\n\n\n<li>Shawn: ((-6, 0))<\/li>\n<\/ul>\n\n\n\n<p>Substitute these into the formula:<\/p>\n\n\n\n<p>[<br>d = \\sqrt{(-6 &#8211; 0)^2 + (0 &#8211; 7)^2}<br>]<br>[<br>d = \\sqrt{(-6)^2 + (-7)^2}<br>]<br>[<br>d = \\sqrt{36 + 49}<br>]<br>[<br>d = \\sqrt{85}<br>]<br>[<br>d \\approx 9.2 \\, \\text{feet}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Conclusion<\/h3>\n\n\n\n<p>The distance between Maria and Shawn is approximately <strong>9.2 feet<\/strong>.<\/p>\n\n\n\n<p>This distance is derived using basic geometry and the distance formula, which calculates the straight-line distance between two points on a coordinate plane. By organizing the positions of the dancers and applying the formula correctly, we arrive at the solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Three ballet dancers are position on stage. If Tina is 7 feet straight behind Maria and 6 feet directly left of Shawn, how far is Maria from Shawn? If necessary, round to the nearest tenth. The Correct Answer and Explanation is: To solve this problem, we need to determine the distance between Maria and Shawn [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-167244","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=167244"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167244\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}