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Algebra 1 Predicting Patterns & Examining Experiments

This unit focuses on changing patterns and examining experiments in Algebra. In section 3, we explore finding points on a line y=3 that are 10 units away from (2, -3). We will also discover points on the y-axis that are 9 units away from (7, 5). Additionally, we will find lattice points that are exactly 10 units away from the origin (0, 0) and explore the distance between lines with different slopes.

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Algebra 1 Predicting Patterns & Examining Experiments

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  1. Algebra 1Predicting Patterns & Examining Experiments Unit 5: Changing on a Plane Section 3: Into the Lattice

  2. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 (2,–3)

  3. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 10 10 (2,–3)

  4. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 (2,3) 6 10 10 (2,–3)

  5. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 (2,3) 6 10 10 (2,–3)

  6. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 –8 (2,3) +8 6 10 10 (2,–3)

  7. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). y=3 (–6,3) –8 (2,3) +8 (10,3) 6 10 10 (2,–3)

  8. Ten Away Find both points on the line y=3 that are 10 units from (2,–3). The two points are (–6,3) and (10,3). y=3 (–6,3) –8 (2,3) +8 (10,3) 6 10 10 (2,–3)

  9. Nine Away What two points on the y-axis are nine units away from (7,5)? (7,5)

  10. Nine Away What two points on the y-axis are nine units away from (7,5)? (7,5) 7

  11. Nine Away What two points on the y-axis are nine units away from (7,5)? 9 (7,5) 7 9

  12. Nine Away What two points on the y-axis are nine units away from (7,5)? 9 9 y (7,5) 7 7 9

  13. Nine Away What two points on the y-axis are nine units away from (7,5)? 9 9 y (7,5) 7 7 9

  14. Nine Away What two points on the y-axis are nine units away from (7,5)? 9 9 y (7,5) 7 7 9 The two points are:

  15. Nine Away What two points on the y-axis are nine units away from (7,5)? 9 9 y (7,5) 7 7 9 The two points are:

  16. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (1,2) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them?

  17. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (2,1) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them?

  18. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (2,1) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them?

  19. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (2,1) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them? distance?

  20. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (2,1) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them? distance at x=2 : y=.4(2-2)+1= 0+1 =1 y=.4(2)=.8 distance = 1–.8 = .2 distance at x=0 : y=.4(0-2)+1= –.8 =.2 y=.4(0)=0 distance = .2–0 = .2

  21. How far apart are the lines? Draw a line through the origin with a slope of 0.4 . Now, draw another line through (2,1) with a slope of 0.4 . What are the equations of these two lines and what is the vertical distance between them? The distance between the two lines is 0.2 . distance at x=2 : y=.4(2-2)+1= 0+1 =1 y=.4(2)=.8 distance = 1–.8 = .2 distance at x=0 : y=.4(0-2)+1= –.8 =.2 y=.4(0)=0 distance = .2–0 = .2

  22. How far is it? How far is the point (5,5) from the origin? Find two other lattice points in the first quadrant that have the same distance from the origin. (5,5)

  23. How far is it? How far is the point (5,5) from the origin? Find two other lattice points in the first quadrant that have the same distance from the origin. (5,5) √50

  24. How far is it? How far is the point (5,5) from the origin? Find two other lattice points in the first quadrant that have the same distance from the origin. (5,5) √50

  25. How far is it? How far is the point (5,5) from the origin? Find two other lattice points in the first quadrant that have the same distance from the origin. (5,5) √50

  26. How far is it? How far is the point (5,5) from the origin? Find two other lattice points in the first quadrant that have the same distance from the origin. (1,7) (5,5) √50 (7,1)

  27. Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. (8,6) 10

  28. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. (8,6) 10 10 10 (10,0)

  29. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. (8,6) 10 (-10,0) 10 (10,0) 10 (0,-10)

  30. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. (6,8) (8,6) 10 10 (-10,0) (10,0) (0,-10)

  31. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. What do we call the set of all points that are equidistant from one point? (6,8) (8,6) 10 (-10,0) (10,0) (0,-10)

  32. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. What do we call the set of all points that are equidistant from one point? - a circle (6,8) (8,6) 10 (-10,0) (10,0) (0,-10)

  33. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. What do we call the set of all points that are equidistant from one point? - a circle (-6,8) (6,8) (8,6) (-8,6) 10 (-10,0) (10,0) (-8,-6) (8,-6) (-6,-8) (6,-8) (0,-10)

  34. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. Are there any other lattice point solutions? (7,7)? (4,9)? (-6,8) (6,8) (4,9) ? (8,6) (-8,6) (7,7) ? 10 (-10,0) (10,0) (-8,-6) (8,-6) (-6,-8) (6,-8) (0,-10)

  35. (0,10) Find all the 10’s. The distance from (8,6) to the origin is exactly 10 units. Find all lattice points that are also exactly 10 units from the origin. Are there any other lattice point solutions? No. (-6,8) (6,8) (8,6) (-8,6) 10 (-10,0) (10,0) (-8,-6) (8,-6) (-6,-8) (6,-8) (0,-10)

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