Project 6.1: Exploring Points on Line Segments

Name: ____________________ Date: _______________The project provides an opportunity for students to explore various aspects of Midpoints and Other Points on Line Segments

Project Scoring

Section Reference Max Score

Section 1 Midpoints & Graphs 8Section 2 Midpoints & Coordinates 8Section 3 Midpoints & Endpoints 8Section 4 Partitioned Line Segments 8Section 5 Random Questions 8

Creativeness & Neatness (use of color, us of different lines, notations, additional facts, etc.) 10

Scored out of 50 50

Project 6.1: Exploring Points on Line Segments

Midpoint Formula

When given two point, (x1, y1) and (x2, y2), the midpoint is ( x1+x22,y1+ y22 )

Finding a point on a line segment

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Project 6.1: Exploring Points on Line SegmentsSection 1: Finding Midpoints using Graphs.

1. (___, ___) and (___, ___) 2. (___, ___) and (___, ___)

3. (___, ___) and (___, ___) 4. (___, ___) and (___, ___)

5. (___, ___) and (___, ___) 6. (___, ___) and (___, ___)

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Midpoint = Midpoint =

Midpoint = Midpoint =

Midpoint = Midpoint =

Project 6.1: Exploring Points on Line SegmentsSection 2: Finding Midpoints from Coordinates7. (9,8) & (-7,16) 8. (11,-3) & (-15,17)

9. and

10. (8.16, 12.47) & (-7.22, 1.40)

11. ( ¾, 12¼) & (-¼, 18) 12. (-15½, 22) & (15.25, 4.75)

Section 3: Finding Endpoint given the midpoint & the other endpoint of the line segment13. Midpoint (-4,6)

Endpoint (2,1)14. Midpoint (-3,3)

Endpoint (-4,-2)

15. Midpoint (32 , 1)Endpoint (5,-7)

16. Midpoint (-3.27,3.88)Endpoint (-4.22,-2.13)

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Project 6.1: Exploring Points on Line SegmentsSection 4: Finding Partitioned Points on a Line Segment

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Project 6.1: Exploring Points on Line SegmentsSection 5: Random Questions

Watch the directions of the line segment!!

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Project 6.1: Exploring Points on Line Segments

Project 6.1: Exploring Points on Line Segments

KEY

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Project 6.1: Exploring Points on Line SegmentsSection 1:1. A (-3, 4); B (5,-6) Midpoint = (1, -1)

2. A (-5, -3); B (3,5) Midpoint = (-1, 1)

3. A (4, -3); B (4,5) Midpoint = (4, 1)

4. A (-6, -3); B (3,-3) Midpoint = (-1½, -3)

5. A (-3, 0); B (6,1) Midpoint = (1½, ½ )

6. A (-1, 7); B (1,-4) Midpoint = (0, 1½)

Section 2: 7. Midpoint = (1,12)

8. Midpoint = (-2, 7)

9. Midpoint = (32, -1)

10. Midpoint = (0.47, 6.935)

11. Midpoint = ( 14 , 15 18 )

12. Midpoint = (-0.125, 13.375)

Section 3:

13. Distance of “x” = -6. Distance of “y” = 5. Endpoint = (-4-6, 6+5) = (-10,11)

14. Distance of “x” = 1. Distance of “y” = 5. Endpoint = (-3+1, 3+5) = (-2,8)

15. Distance of “x” = -3.5. Distance of “y” = 8. Endpoint = ( 32−72 , 1+8) = (-2,9)

16. Distance of “x” = 0.95. Distance of “y” = 6.01. Endpoint = (-3.27+0.95, 3.88+6.01) = (-2.32,9.89)

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Project 6.1: Exploring Points on Line SegmentsSection 4:17. A (1,2); B (6,12). Distance of “x” = 5. Distance of “y” = 10.

Point Q: ( 1 + 15

(5), 2 + 15

(10) ) = (2, 4).

18. C (-6,0); D (3,6). Distance of “x” = 9. Distance of “y” = 6Point Q: ( -6 + 2

3 (9), 0 + 2

3 (6) ) = (0, 4).

19. F (-3,-4); G (5,4). Distance of “x” = 8. Distance of “y” = 8.Partition is 1:3, so the point Q is ¼ of the distance between F and G from F.Point Q: ( -3 + 1

4 (8), -4 + 1

4 (8) ) = (-1, -2).

20. J (-5, 4); K (5, -1). Distance of “x” = 10. Distance of “y” = 5.Partition is 3:2, so the point Q is 3

5 of the distance between J and K from J.

Point Q: ( -5 + 35

(10), 4 + 35

(5) ) = (1, 7).

Section 5:21. X (-6,2); Y (6,-10). Distance of “x” = 12. Distance of “y” = -12.

NOTE: The direction of the line segment is XY.Point P: (-6 + 1

3 (12), 2 + 1

3 (-12) ) = (-2, -2).

22. Y (6,-10); X (-6,2). Distance of “x” = -12. Distance of “y” = 12.Partition is 3:1, so the point Q is 3

4 of the distance between Y and X from Y.

NOTE: The direction of the line segment is YX.Point Q: (6 + 3

4 (-12), -10 + 3

4 (12) ) = (-3, -1).

23. A (1,4) and P (3,5). Distance of xAP is +2. Distance of yAP is +1P is 1/3 the distance from A to B. So, B is 2/3 from P.Point B = P (3,5) + 2 times the distances from AP.Point B = (3 + 2(2), 5 + 2(1) ) = (7,7).

Check: P = A (1,4) + 13

distance to B (7,7) = (1 + 13

(6), 4 + 13

(3) ) = (3, 5).

24. C (0,0) and Q (-1,-2). D = Q (-1, -2) + 6 times distance from CQ.Point D = (-1 + 6(-1), -2 + 6(-2)) = (-7, -14)

Check: Q = 17

distance from C D. Q = (0 + 17

(-7), 0 + 17

(-14)) = (-1, -2).

25. J (5,-1); H (-5, -6). JH. Distance of “x” = -10. Distance of “y” = -5.

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Project 6.1: Exploring Points on Line Segments

Point Q = (5 + 45

(-10), -1 + 45

(-5) ) = (-3, -5).

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