Points, lines and rectangles
- Bernard Murphy
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. 1. A:(0,5) and B:(10,0). Find the coordinates of C and D. 2. The line AB has equation y=-0.5x+6. What is the equation of the line BC? 3. D:(-3,0) and B:(12,0). What is the area of the rectangle? 4. The rectangle has area 40 square units. Give a possible equation for line AB. You might like to work on one or more of these problems before using the instructions below to explore these using GeoGebra.
Enter y=x-1 in the Input bar. Select the Point tool and click on points with coordinates (4,-1) and (7,2). You might need to use the Move Graphics View tool . Next select the Line tool and click on the two points above in turn. Select the Perpendicular line tool , 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. You should now see this:
Select the Intersect tool and then click on two intersecting lines; their point of intersection will appear. Repeat so that the four vertices of the rectangle are marked. Finally select the Polygon tool 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 of all four lines and the area of the rectangle: poly1 is 12 square units.
You are now ready to tackle the four problems above.