The diagram shows a rectangle, ABCD, along with the line through points A and B.

Here are four problems, each relating to different sized rectangles ABCD, where points A, B and D each lie on an axis as shown above.[br][br]1. A:(0,5) and B:(10,0). Find the coordinates of C and D.[br][br]2. The line AB has equation y=-0.5x+6. What is the equation of the line BC? [br][br]3. D:(-3,0) and B:(12,0). What is the area of the rectangle?[br][br]4. The rectangle has area 40 square units. Give a possible equation for line AB. [br][br]You might like to work on one or more of these problems before using the instructions below to explore these using GeoGebra. [br]

Enter y=x-1 in the Input bar.[br]Select the Point tool  [icon]/images/ggb/toolbar/mode_point.png[/icon]  and click on points with coordinates (4,-1) and (7,2). You might need to use the Move Graphics View tool [icon]/images/ggb/toolbar/mode_translateview.png[/icon].[br]Next select the Line tool [icon]/images/ggb/toolbar/mode_join.png[/icon]and click on the two points above in turn.[br]Select the Perpendicular line tool [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon], click on one of the two points and then on one of the parallel lines. Next click on the other point and again on one of the parallel lines. [br]You should now see this:

Select the Intersect tool [icon]/images/ggb/toolbar/mode_intersect.png[/icon] and then click on two intersecting lines; their point of intersection will appear. Repeat so that the four vertices of the rectangle are marked. [br][br]Finally select the Polygon tool [icon]/images/ggb/toolbar/mode_polygon.png[/icon] and click on the four vertices of the rectangle in turn, starting and ending with the same vertex. 

Notice what is happening in the Algebra View; in particular you will see the equations[br]of all four lines and the area of the rectangle: poly1 is 12 square units. [br][br][b][center][b]Y[/b][b]ou are now ready to tackle the four problems above.[/b][/center][/b][br]