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(:title Cartesian Coordinates in the Plane - 2D Horizontal and Vertical Distance :) >>nav_bar<< %reg%Mathcasts         %exa%Examples      %pra%Practice%%    %mor%More      %up%[[glossary/C|C]] >><< [[<<]] [table border=1 cellpadding=3 width=100%] [row] []>>&<< %ref b%Definition:%% The %red b%Cartesian Coordinate System%% is the %c11%''rectangular''%% system of locating points in the plane. >>&<< %reg b%Rule:%% A point (x,y) is located by finding its horizontal x-coordinate and its vertical y-coordinate. >>&<< %newwin%[[http://mathcasts.org/gg/enliven/af/coor/coor1/coor1-1.html|%exa b%Review%% - Animated and Interactive Review of Locating Points in the First and Four Quadrants%%]] [tableend] >>-<< [table border=1 cellpadding=3 width=100%] [row] []>>&<<%c11 exa%InterActivities: Plotting Points and Drawing Basic 2D Shapes %% >>&<< (:showhide init=show div=div111 lshow="+" lhide="-":) %sol%(:showhide init=hide div=div1111 lshow="+" lhide="-":) Interactivity 1 (:showhide init=hide div=div1112 lshow="+" lhide="-":) %exa%%ans%Interactivity 2%%%% (:showhide init=hide div=div1113 lshow="+" lhide="-":) %ref%Interactivity 3%% (:showhide init=hide div=div1114 lshow="+" lhide="-":) %exa%Interactivity 4%% >>&<< (:div111 id=div111 style="margin-left:15px":) (:div1111 id=div1111 :) [table border=2 bgcolor=#fafafa width="98%" cellpadding=3 class=s9] [row] [] 1. Click on the %ref%New point%% Attach:GgbActivity./point.jpg tool. In the drawing pad, find the point with coordinates (1,1) and then click. Point A should be drawn. Check the coordinates of point A by rolling your mouse over it.%% >>&<< 2. Find the coordinates and draw the point B(1,4). Is B %exa%above%% or %up%right of%% A? (:showhide init=hide div=div7111 lshow="+" lhide="above":) >>&<< 3. Find the coordinates and draw the points C(5,4) and D(5,1).%% >>&<< 4. Use the %ref%Segment%% Attach:GgbActivity./segment.jpg tool and make the rectangle ABCD. >>&<< 5. What is the width and height of the rectangle ABCD? (:showhide init=hide div=div7112 lshow="+" lhide="w=4 and h=3":) [tableend] >>&<< (:div1111end:) (:div1112 id=div1112 :) [table border=1 bgcolor=#fafffa width="98%" cellpadding=3 class=s9] [row] [] 1. Click on the %ref%Reset%% Attach:GgbActivity./reset.jpg button to clear the drawing pad.%% >>&<<2. Find and draw the points A(5,0), B(1,3) and C(1,0)%% >>&<<3. Use the %ref%segment%% tool Attach:GgbActivity./segment.jpg to make the triangle ABC. What kind of triangle is ΔABC? (:showhide init=hide div=div7113 lshow="+" lhide=" right ":) >>&<<4. From the coordinates, can you find the lengths of {$ \overline {CA} $} and {$ \overline {CB} $}? (:showhide init=hide div=div7114 lshow="+" lhide=" 4 and 3  ":) >>&<<5. Using Pythagoras' theorem, what is the length of {$ \overline {AB} $}? (:showhide init=hide div=div7115 lshow="+" lhide=" 5 ":) >>&<<  To check your work, click on View -> Algebra Window. [tableend] >>&<< (:div1112end:) (:div1113 id=div1113 :) [table border=1 bgcolor=#fafaff width="98%" cellpadding=3 class=s9] [row] [] 1. Click on the %ref%reset%% button to clear the drawing pad. >>&<<2. Click on the %ref%Move drawing pad%% tool Attach:GgbActivity./move_dp_s.jpg and then click and drag on (0,0) to put it in the middle of the drawing pad.%% >>&<<3. Find and draw the points A(-2,-1), B(1,-4) and C(1,1)%% >>&<<4. Use the %ref%segment%% tool Attach:GgbActivity./segment.jpg to make the triangle ABC. >>&<<5. Click on View -> Algebra Window. You should see 3 free points and 3 dependent line segments: a, b and c. >>&<<6. Click on the %ref%Move%% Attach:GgbActivity./move.jpg tool and click and drag C until ABC is an isosceles triangle. (:showhide init=hide div=div11131 lshow="+" lhide="-":) %dkr%Answers:%% (:div11131 id=div11131 style="margin-left:15px":) Isosceles triangle means 2 equal sides so we want two of a, b or c to be the same. Try C=(0,2). Can you find another point? (There are many, many points.) %dkr%Another point:%% (:showhide init=hide div=div7116 lshow="+" lhide=" (1,3) ":) (:div11131end:) [tableend] >>&<< (:div1113end:) (:div1114 id=div1114 :) [table border=1 bgcolor=#fffafa width="98%" cellpadding=3 class=s9] [row] [] To clear the drawing pad, click on the %ref%Reset%% Attach:GgbActivity./reset.jpg button.%% >>&<<1%exa%a.%% Draw A(0,3) and B(4,1). %exa%b.%% Find a point C (there are 2!) to make triangle ABC a right-triangle%% >>&<<  %exa%c.%% Connect A, B and C with line segments. %exa%d.%% Use Pythagoras' theorem to check that {$ \overline {AB} $} is the "correct" length! >>&<<2%exa%a.%% Clear your drawing pad. %exa%b.%% Draw A(1,1) and B(4,3). %exa%c.%% Determine and draw the points C and D that make ACBD a rectangle.%% [tableend] >>&<< (:div1114end:) >>&<< (:div112end:) (:applet code="geogebra.GeoGebraApplet" codebase="Java/GeoGebra/" archive="http://www.geogebra.org/webstart/3.2/geogebra.jar" width="810" height="400" filename="http://mathcasts.org/mtwiki/uploads/GlossaryT/cart_coor1.ggb" showResetIcon="true" showToolBar="true" showMenuBar="true":) >>&<< (:div111end :) >>&<< [tableend] (:if false:) >>-<< [table border=1 cellpadding=3 width=100%] [row] [] (:showhide init=show div=div1 lshow="+" lhide="-":) Examples                          (:div1 id=div1 style="margin-left:15px":) * (x,y)=(horizontal,vertical) (Remember: in English "h" is before "v"). >>&<< (:div1end :) %exa%Possible continuations:%% Quadrant 1: Higher or wider? Quadrant 1: Points - Find their coordinates Quadrant 1: Making dynamic right-triangles using x(A) and y(B); dynamic rectangles... Quadrants 4: What quadrants? Quadrants 4: Points - Find their coordinates >>-<< [tableend] (:ifend:) (:div7111 id=div7111 :) (:div7111end:) (:div7112 id=div7112 :) (:div7112end:) (:div7113 id=div7113 :) (:div7113end:) (:div7114 id=div7114 :) (:div7114end:) (:div7115 id=div7115 :) (:div7115end:) (:div7116 id=div7116 :) (:div7116end:) (:div7117 id=div7117 :) (:div7117end:) >>-<< ---- >>&<< %rel%Related Topics *[[glossaryT/cartcoor|Cartesian Coordinates - Definitions & Rules]] - %s9 sol%under construction%% *[[interA/cartcoor1|Cartesian Coordinates 1 - InterActivities for Plotting Points]] *[[glossaryT/lineGraph|Line Graphs - Plotting Points]] - %s9 sol%link fixed: September 27%% >>&<< ---- >>&<< (:showhide init=hide div=div9 lshow="+" lhide="-":) Metadata (:div9 id=div9 :) [table class=column border=1 width=100% cellpadding=3] [row] [ width=110px] '''Global''' []Cartesian Plane [row] []Brief []Interactivities involving understanding the Cartesian plane coordinate system [row] []Grade []4-10    Interactivities can be used from 4th grade level on up [row] []Strand []Algebra and Functions / Geometry and Measurement [row] []Standard []%popwin%[[standards/CA4MG-2-0?action=popopen|CA 4MG2.0]],%popwin%[[standards/CA4MG-2-1?action=popopen|CA 4MG2.1]], %popwin%[[standards/CA4MG-2-2?action=popopen|CA 4MG2.2]], %popwin%[[standards/CA4MG-2-3?action=popopen|CA 4MG2.3]], %popwin%[[standards/CA5AF-1-4?action=popopen|CA 5AF1.4]], , %popwin%[[standards/ACTgr28?action=popopen|ACT GR 28-32]] [row] []Keywords []cartesian plane, coordinates, points, grid, x-coordinate, y-coordinate [row] []Comments []none [row] []Download [][[http://www.geogebra.org|GeoGebra]] is freeware that can be used offline. After installing GeoGebra, go to the InterActivity and select command: %red%File -> Save%%. %s9 sol%If there is no command menu, just double-click on the InterActivity. It will open in a new window with command menu.%% [row] []Author []LFS - [[mailto:emath@emathforall.com?subject=ggb_slopes|contact]] - [[http://math247.pbwiki.com/Algebra-with-GeoGebra|website]] [row] []Type []Freeware - Available for Offline and Online Use - Translatable (html) [row] []Use []Requires [[http://www.java.com/en/download/index.jsp|sunJava player]] [tableend] (:div9end:) >>-<< [table width=100%] [row] [][[Glossary/C| Attach:main/tri_purple_up_a.gif ]] [[Glossary/C| Up one level]] [r](:html:) (:htmlend:) [tableend]