1. 2.5 Distance on the Plane: Finding the Length of a Line Segment for Any Two Points and Classifying Triangles

2. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Learning Goal for Today: Investigate how to find the length of a line segment for any two points

3. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Mary, who is a sheep farmer, had a little lamb Mary lives at 8 th avenue and 9 th street. These coordinates are shown as (8, 9). Where Mary lives all avenues run north south and all streets run east and west. Farmers are allowed to cut across properties and don’t have to stay on the streets or avenues with their sheep because of grazing rights

4. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (8,9)

5. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Mary has to take her little lamb, George, to Lambs are us to get a haircut (called shearing) at Lambs ‘R’ Us so that George can sell the wool for money to go on a school trip Lambs ‘R’ Us is located at (1, 2)

6. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (8,9) (1,2)

9. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Your job is to find the best way to get there Step 1 – work with an elbow partner to discuss the best way. Be sure you can explain why Step 2 – Work with your quad to see if you all agree. If you do. Why? If you don’t. Why not? If you don’t agree, try and come to an agreement.

10. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (8,9) (1,2)

11. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Once your quad is in agreement, take a piece of large chart paper and put your solution on it Make sure you don’t put your names on it You must include a diagram Tape your paper up in a corner alone, if you think you have a unique solution, or with other similar papers

12. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Now, everyone up and look at everyone else’s solutions

13. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Go stand by the solution you like the best

14. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (8,9) (1,2)

15. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Mary stops to talk to a friend at point (5, 6). Has she reached the ½ way point? Why or why not?

16. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (8,9) (1,2) (5,6)

17. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Can we come up with a formula that will work so that we can find the distance between any two points? Lets make one point (x 1, y 1 ) and the other point (x 2, y 2 )

18. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles (x 2, y 2 ) (x 1, y 1 )

19. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles

20. A Triangle has vertices A(-1, -1), B (2,0) and C(1,3) Find the length of the line segments and the slopes and classify the triangle

23. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Triangle TypeLengthsSlopes Scalene Isoceles Equilateral Right

24. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Triangle TypeLengthsSlopes ScaleneAll different Isosceles2 same, 1 different EquilateralAll same Right2 same if right isosceles Or 3 different if not Slopes of 2 sides that are right angles are negative reciprocals of each other

25. 2.5 Distance on the Plane: Finding the Length of a Line Segment and Classifying Triangles Homework: P.162, #2 & p.163, #5, 7, 11 & 19