1. M. Stocking ©2005 Points, Lines, Planes Line Segments and Rays

2. Definitions Point - Line - Plane - A geometric object that has no dimensions, only a location A flat surface that extends endlessly in all directions A collection of points along a straight path having no endpoints

3. M. Stocking ©2005 Definitions Line Segment- Ray - A part of a line that has two endpoints A part of a line that only has one endpoint

4. M. Stocking ©2005 Graphing Points Points are graphed using coordinates, points can have one, two or three coordinates. Points with one coordinate are often graphed on a number line 0 1234-2-3-45 For Example point A(3) Point name Point Coordinate A Point B(-2) B Point C(4.5) C

5. M. Stocking ©2005 Graphing Points (cont.) Points with two coordinates are graphed on a plane, most often on the x-y plane For Example point A(3,1) Point name Point Coordinates (x, y) x y A B(-2, 4) B C(3, -4) C XY

6. M. Stocking ©2005 Graphing Line Segments Line Segments are graphed by plotting their endpoints then connecting them with the part of a line that lies in between. For Example, with A(2,4) and B (-1, -3) the line segment would be points A and B and all the points on the line in between x y A B Step 1. Plot the endpoints Step 2. Connect with a piece of a line

7. M. Stocking ©2005 Graphing Line Segments (cont.) Given the points C(-3, 4) and D(2,-3) graph the line segment x y Step 1. Plot the endpoints Step 2. Connect with a piece of a line C D Note line segment is the same as line segment

8. M. Stocking ©2005 Graphing Rays Rays are graphed similar to line segments. To graph a ray you must know the coordinate of the endpoint and the coordinate of one other point on the ray. x y For example ray has endpoint G(-3,-4) and goes through point H(4, 2 ) Step 1. Plot the endpoint and other point Step 2. Draw in the ray, making sure to use the correct endpoint G H

9. M. Stocking ©2005 Graphing Rays (cont.) x y G H x y G H Note is NOT the same as

10. M. Stocking ©2005 Graphing Rays (cont.) Graph the ray that has endpoint J (4,5) and goes through point K(-1, 1) x y Step 1. Plot the endpoint and other point Step 2. Draw in the ray, making sure to use the correct endpoint J K

11. M. Stocking ©2005 Notation for Rays, Line Segments and Lines To show that objects are rays, line segments or lines there is special notation that can be used To show a ray with endpoint A that goes through point B a small ray is drawn above the two letters Notice the part of the ray without the arrow goes above the endpoint and the part with the arrow goes above the non endpoint. It is not the same as

12. M. Stocking ©2005 Notation for Line Segments To show a line segment with endpoints A and B a small line with no arrows is drawn above AB It could also be written as

13. M. Stocking ©2005 Notation for Lines Notation for lines is similar to notation for rays and line segments. To show a line going through points A and B a small line is drawn above AB with arrows on each end. It could also be written as

14. M. Stocking ©2005 How to represent a plane A plane is represented by a parallelogram For example plane P is simply shown by P

15. M. Stocking ©2005 Practice Graph the following on a sheet of graph paper using the points at the right A ( -3, -2) B (2, -2) C (3, 4) D (-4, 4) E (-1.5, -0.5) F (0.5, -0.5) G (-1, 1) H (0, 1) I (0, 2) J (-2, 2.5) K (1, 2.5) L (-5, 6) M (-1.5, 6) N (-2, 4) O ( 0.5, 6) P (1, 4) Q (3.5, 6)

16. M. Stocking ©2005 Points, Lines, Planes Activity With a partner create a picture on graph paper using points, line segments, and rays. On another sheet create instructions for someone else using the proper notation for the points, line segments, and rays.