1. Algebra 1 Predicting Patterns & Examining Experiments Unit 5: Changing on a Plane Section 2: Get to the Point

2. Which distance is the greatest? The distance between which two numbers is greatest on the number line? a) 17 and 24 b) 27 and 14 c) –5 and 3 d) 7 and –7 e) 24 and 17 The distance between which two numbers is greatest on the number line? a) 17 and 24 b) 27 and 14 c) –5 and 3 d) 7 and –7 e) 24 and 17

3. Which distance is the greatest? The distance between which two numbers is greatest on the number line? a) 17 and 24 distance = 7 b) 27 and 14 distance = 13 c) –5 and 3 distance = 8 d) 7 and –7 distance = 14 e) 24 and 17 distance = 7 The distance between which two numbers is greatest on the number line? a) 17 and 24 distance = 7 b) 27 and 14 distance = 13 c) –5 and 3 distance = 8 d) 7 and –7 distance = 14 e) 24 and 17 distance = 7

4. Which distance is the greatest? The distance between which two numbers is greatest on the number line? a) 17 and 24 distance = 7 b) 27 and 14 distance = 13 c) –5 and 3 distance = 8 d) 7 and –7 distance = 14 e) 24 and 17 distance = 7 The distance between which two numbers is greatest on the number line? a) 17 and 24 distance = 7 b) 27 and 14 distance = 13 c) –5 and 3 distance = 8 d) 7 and –7 distance = 14 e) 24 and 17 distance = 7

5. What is the shortest distance? Place each fraction at its location on the number line. Then, find the distance between the two that are the closest.

6. What is the shortest distance? Place each fraction at its location on the number line. Then, find the distance between the two that are the closest.

7. What is the shortest distance? Place each fraction at its location on the number line. Then, find the distance between the two that are the closest.

8. What is the shortest distance? Place each fraction at its location on the number line. Then, find the distance between the two that are the closest.

9. What is the shortest distance? Place each fraction at its location on the number line. Then, find the distance between the two that are the closest. The shortest distance is.002, which is 1/450. Place each fraction at its location on the number line. Then, find the distance between the two that are the closest. The shortest distance is.002, which is 1/450.

10. Which point is the furthest from the y-axis? A:(5,6) B:(-6,5) C:(-3,-7) D:(7,-3)

11. Which point is the furthest from the y-axis? A:(5,6) B:(-6,5) C:(-3,-7) D:(7,-3) y-axis AB C D

12. Which point is the furthest from the y-axis? A:(5,6) B:(-6,5) C:(-3,-7) D:(7,-3) The point D is the furthest from the y-axis. A:(5,6) B:(-6,5) C:(-3,-7) D:(7,-3) The point D is the furthest from the y-axis. y-axis AB C D 5 6 3 7

13. Which point is the furthest from (2,5)?

14. Distance Formula

15. Find the distance from A to B. d

16. 5 – 3 = 2 7 – 2 = 5 d

17. Find the distance from A to B. 2 5 d

18. 2 5 d ≈ 5.385

19. It’s just pythagorean theorem with coordinates plugged in... Find the distance from A to B. 2 5 d ≈ 5.385

20. It’s just pythagorean theorem with coordinates plugged in... Find the distance between the two points. d 11 22

21. It’s just pythagorean theorem with coordinates plugged in... Find the distance from A to B. d 11 22 y - y x - x 21 21

22. It’s just pythagorean theorem with coordinates plugged in... Find the distance from A to B. d 11 22 y - y x - x 21 21

23. It’s just pythagorean theorem with coordinates plugged in... Find the distance from A to B. d 11 22 y - y x - x 21 21

24. The Distance Formula: (It’s just pythagorean theorem with coordinates plugged in...) The Distance Formula: (It’s just pythagorean theorem with coordinates plugged in...) Find the distance from A to B. d 11 22 y - y x - x 21 21

25. The Distance Formula: (It’s just pythagorean theorem with coordinates plugged in... So, either use the formula or the theorem to find distances.) The Distance Formula: (It’s just pythagorean theorem with coordinates plugged in... So, either use the formula or the theorem to find distances.) Find the distance from A to B. d 11 22 y - y x - x 21 21

26. Which point is the furthest from (2,5)? √13 ≈ 3.606

27. Which point is the furthest from (2,5)? √13 ≈ 3.606

28. Which point is the furthest from (2,5)? NOTICE THE TRIANGLES: Which point is the furthest from (2,5)? NOTICE THE TRIANGLES: Which point is the furthest from (2,5)? √13 ≈ 3.606

29. Which point is the furthest from (2,5)? All distances are the same, so no point is the furthest. Which point is the furthest from (2,5)? All distances are the same, so no point is the furthest. Which point is the furthest from (2,5)? √13 ≈ 3.606

30. Do the three points below form a Right triangle?

31. The theorem says, if you have a Right triangle, then, the sum of the squares of the legs is equal to the square of the hypotenuse. But, the opposite is also true, if the sum of the squares of the legs is equal to the square of the hypotenuse, then, you have a Right triangle. The theorem says, if you have a Right triangle, then, the sum of the squares of the legs is equal to the square of the hypotenuse. But, the opposite is also true, if the sum of the squares of the legs is equal to the square of the hypotenuse, then, you have a Right triangle. A Note on the Pythagorean Theorem

32. Do the three points below form a Right triangle? A:(0,2) B:(4,5) C:(6,-6)

33. Pythagorean thm. is true, so we it is a Right triangle. Do the three points below form a Right triangle? A:(0,2) B:(4,5) C:(6,-6)