Practice problems for distance on the number line. This is for high school students.

1. Millau Bridge Sir Norman Foster Point, Lines, Planes, Angles Fallingwaters Frank Lloyd Wright Millenium Park Frank Lloyd Wright 1.3 CE Page 14

2. 1.3 CE Page 14 1. Does the symbol represent a line, segment, ray or length? 2. How many endpoints does a segment have? A ray? A line? a] b] c] d] Segment Line Ray Length 2 1 0 or none. A B A A B B

3. 3. Is the same as ? 4. Is the same as ? 5. Is the same as ? 6. Is the same as ? A B Yes Yes Yes No

4. 7. What is the coordinate of P? of R? P Q R S T 0 1 2 -2 -1 8. What is the point with the coordinate of 2? 9. Find each distance a] RS b] RQ c] PT . 10. Name three segments congruent to . -2 0 T 1 1 QR, RS, ST Reversing the letters are alternative answers.

5. 11. Name a ray opposite . P Q R S T 0 1 2 -2 -1

6. 11. Name a ray opposite . P Q R S T 0 1 2 -2 -1 12. Name the midpoint of . R

7. 11. Name a ray opposite . P Q R S T 0 1 2 -2 -1 12. Name the midpoint of . 13. a] What is the number that is half way between 1 and 2? b] What is the coordinate of the midpoint of ? R 1.5

8. 11. Name a ray opposite . P Q R S T 0 1 2 -2 -1 12. Name the midpoint of . 13. a] What is the number that is half way between 1 and 2? b] What is the coordinate of the midpoint of ? R 1.5 1.5

9. P Q R S T 0 1 2 -2 -1 14. a] Could you list all the numbers between 1 and 2? b] Is there a point on the number line for every number between 1 and 2? c] Is there a limit to the number of points between 1 and 2? No Yes No There are an infinite number of fractions between 1 and 2. There is always a point between any two points on the segment ST. The point in between is the midpoint.

10. State whether the figures appear to be congruent (that is, appear to have the same size and shape. 16. No No Yes Yes Yes, mirror line Yes, mirror line Not the same size. Note the same shape.

11. 21. Draw 2 points P and Q on a sheet of paper. Fold the paper so that the fold line f contains both P and Q. Now fold so that P falls on Q. Call the second fold g. Lay the paper flat and label the intersection of f and g as point X. How are points P, Q and X related? Explain? X is the midpoint of PQ because …

12. 22. If AB = BC, must point B be the midpoint of . Explain. A C B 1 B 2 B 3 B 5 B 4 There are an infinite number of points that will work that are not midpoints. All of them are on the red line.

13. Given the numbers are coordinates of two points on a number line. State the distance between the points. 23 . -2 and 6. 24 . -2 and - 6. 25 . 2 and - 6. 26 . 7 and -1.

14. C’est fini. Good day and good luck.