Placing Figures in the Coordinate Plane

1. Placing Figures in the Coordinate Plane

2. Placing Figures in the Coordinate Plane. • Why do we want to do this? • To have a working picture with which we can discover new rules and prove theorems. • How do we place a figure in the coordinate plane? • Consider the rules and definitions of the figure. • Label the points according to their rules. • Use the minimum number of letters possible.

3. Name the Missing Coordinates of the Rectangle. In this example, we will take advantage of the symmetry in a rectangle. ( -a , b ) ( a , b ) b b a a b b ( -a , -b ) ( a , -b )

4. Name the Missing Coordinates of the Rectangle. ( 0 , b ) In this example, we will use the origin to minimize the number of letters needed. ( a , b ) b b a ( 0 , 0 ) ( a , 0 )

5. Name the Missing Coordinates of the Kite. In this example, we will take advantage of the symmetry along one axis of a kite. ( 0 , b ) b ( -a , 0 ) ( a , 0 ) a a c (0, -c)

6. Name the Missing Coordinates of the Parallelogram. An ordinary parallelogram has no lines of symmetry so we will place one point on the origin. ( c , b ) ( a+c , b ) b b c c a ( 0 , 0 ) ( a , 0 )

7. Name the Missing Coordinates of the Isosceles Trapezoid. In this example we will place one point of the isosceles trapezoid at the origin. ( b , c ) ( a-b , c ) c c b b ( 0 , 0 ) ( a , 0 )

8. Find the length and midpoint of the leg on the right. The leg has points (a-b , c) and (a , 0). The distance between the points is The midpoint between the points is ( b , c ) ( a-b , c ) ( 0 , 0 ) ( a , 0 )

9. Homework • P 328 (1-12). Please draw all pictures.