{"id":1406,"date":"2020-07-11T07:05:08","date_gmt":"2020-07-11T05:05:08","guid":{"rendered":"http:\/\/mathe-lernen.net\/?p=1406"},"modified":"2026-05-15T17:17:06","modified_gmt":"2026-05-15T15:17:06","slug":"abstand-von-punkten-im-koordinatensystem","status":"publish","type":"post","link":"https:\/\/mathe-lernen.net\/?p=1406","title":{"rendered":"Abstand von Punkten im Koordinatensystem"},"content":{"rendered":"\n<p><img loading=\"lazy\" decoding=\"async\" width=\"50\" height=\"50\" class=\"wp-image-7501\" style=\"width: 50px;\" src=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png\" alt=\"\" srcset=\"https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2.png 100w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-80x80.png 80w, https:\/\/mathe-lernen.net\/wp-content\/uploads\/2024\/06\/award2-50x50.png 50w\" sizes=\"auto, (max-width: 50px) 100vw, 50px\" \/><\/p>\n\n\n\n<p class=\"has-background\" style=\"background-color:#b7d7e3\"><strong>Denk Dir den Abstand zwischen A und B als Hypotenuse in einem rechtwinkligen Dreieck. <br><\/strong>$$\\overline{AB}=\\sqrt{(x_{Abstand})\u00b2 + (y_{Abstand})\u00b2}$$<br><br>1.Verfolge die Entstehung des rechtwinkligen Dreiecks. <br>2.Notiere die L\u00e4ngen der Katheten. <br>   Sie ergeben sich aus den L\u00e4ngen der Horizontalen und der Vertikalen.<br>4.Notiere eine Rechnung f\u00fcr die Hypotenuse (Abstand der Punkte). Rechne!<\/p>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Press the MOVE button below. Watch what happens. Then answer the question that follows.\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/zyrfvz8w\/width\/743\/height\/611\/border\/888888\/sfsb\/true\/smb\/false\/stb\/true\/stbh\/false\/ai\/false\/asb\/true\/sri\/false\/rc\/true\/ld\/true\/sdz\/true\/ctl\/false\" width=\"743px\" height=\"611px\" style=\"border:0px;\"> <\/iframe>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Move the 2 points wherever you'd like! Press MOVE.  Then CONTINUE. \" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/my8dcfbk\/width\/686\/height\/585\/border\/888888\/sfsb\/true\/smb\/false\/stb\/true\/stbh\/true\/ai\/false\/asb\/true\/sri\/false\/rc\/false\/ld\/true\/sdz\/true\/ctl\/false\" width=\"686px\" height=\"585px\" style=\"border:0px;\"> <\/iframe>\n\n\n\n<iframe loading=\"lazy\" scrolling=\"no\" title=\"Abst\u00e4nde im Koordinatensystem berechnen\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/w5m2wmjx\/width\/800\/height\/600\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/false\/rc\/false\/ld\/false\/sdz\/false\/ctl\/false\" width=\"800px\" height=\"600px\" style=\"border:0px;\" allowfullscreen=\"\"> <\/iframe>\n\n\n\n<p class=\"has-background\" style=\"background-color:#b3e9ff\"><strong>Und nun im 4-Quadranten- Koordinatensystem&#8230;<\/strong><br><br>Klick &#8222;Show Hints&#8220; f\u00fcr den Anfang. <br>Dort kannst Du auch das Ergebnis kontrollieren.<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\"><iframe loading=\"lazy\" scrolling=\"no\" title=\"Distance in the Coordinate Plane (With Hints)\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/xtjh8eyd\/width\/758\/height\/523\/border\/888888\/sfsb\/true\/smb\/false\/stb\/false\/stbh\/false\/ai\/false\/asb\/false\/sri\/true\/rc\/false\/ld\/true\/sdz\/true\/ctl\/false\" width=\"758px\" height=\"523px\" style=\"border:0px;\"> <\/iframe>\n\nAutor:\n<a href=\"https:\/\/www.geogebra.org\/u\/tbrzezinski\">Tim Brzezinski<\/a>, geogebra.org<\/pre>\n<div class=\"pvc_clear\"><\/div><p id=\"pvc_stats_1406\" class=\"pvc_stats all  \" data-element-id=\"1406\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p><div class=\"pvc_clear\"><\/div> ","protected":false},"excerpt":{"rendered":"<p>Denk Dir den Abstand zwischen A und B als Hypotenuse in einem rechtwinkligen Dreieck. $$\\overline{AB}=\\sqrt{(x_{Abstand})\u00b2 + (y_{Abstand})\u00b2}$$ 1.Verfolge die Entstehung des rechtwinkligen Dreiecks. 2.Notiere die L\u00e4ngen der Katheten. Sie ergeben sich aus den L\u00e4ngen der Horizontalen und der Vertikalen.4.Notiere eine Rechnung f\u00fcr die Hypotenuse (Abstand der Punkte). Rechne! Und nun im 4-Quadranten- Koordinatensystem&#8230; Klick &#8222;Show Hints&#8220; f\u00fcr den Anfang. Dort<\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_1406\" class=\"pvc_stats all  \" data-element-id=\"1406\" style=\"\"><i class=\"pvc-stats-icon small\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/mathe-lernen.net\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[987,52],"tags":[124,157,158,159,160,161,162,267,308,398,586],"class_list":["post-1406","post","type-post","status-publish","format-standard","hentry","category-pythagoras","category-rechtwinklige-dreiecke","tag-dreieck","tag-hypotenuse","tag-kathete","tag-pythagoras","tag-satz","tag-rechter-winkel","tag-rechtwinklig","tag-koordinatensystem","tag-trigonometrie","tag-punkt","tag-abstand"],"a3_pvc":{"activated":true,"total_views":331,"today_views":0},"_links":{"self":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1406","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1406"}],"version-history":[{"count":5,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1406\/revisions"}],"predecessor-version":[{"id":9742,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=\/wp\/v2\/posts\/1406\/revisions\/9742"}],"wp:attachment":[{"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathe-lernen.net\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}