The document discusses finding the midpoint of a line segment on a number line and on a coordinate plane. It defines the midpoint as the point that bisects the segment. It provides formulas for calculating the x- and y-coordinates of the midpoint given the endpoints' coordinates. Several examples are worked through, finding midpoints of segments with given endpoints on a coordinate plane using the midpoint formulas.

1. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn B A C

2. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn The midpoint of a line segment, , is the point C that ______ the segment. B A C

3. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects The midpoint of a line segment, , is the point C that ______ the segment. B A C

4. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C

5. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C

6. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 = (-2) ÷ 2 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C

7. Midpoints You will learn to find the coordinates of the midpoint of a segment. What You'll Learn bisects C = [3 + (-5)] ÷ 2 = (-2) ÷ 2 = -1 The midpoint of a line segment, , is the point C that ______ the segment. B A C -7 -6 -5 -4 -2 -3 0 -1 1 2 3 4 5 6 7 A B C

8. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5

9. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5

10. Midpoints On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is Theorem 2 – 5 A B

11. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 A B

12. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 A B

13. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 x A B

14. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x A B

15. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x y A B

16. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. Consider the x-coordinate: It will be ( midway ) between the lines x = 1 and x = 9 Consider the y-coordinate: It will be ( midway ) between the lines y = 3 and y = 7 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A B x y C(x, y)

17. Midpoints On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6

18. Midpoints On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6

19. Midpoints O y x On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6

20. Midpoints O y x On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1 , y 1 ) and (x 2 , y 2 ) are Theorem 2 – 6

21. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 A(1, 7) B(9, 3)

22. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 x A(1, 7) B(9, 3)

23. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 x y A(1, 7) B(9, 3)

24. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y

25. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y

26. Midpoints Find the midpoint, C(x, y), of a segment on the coordinate plane. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 x = 1 x = 9 y = 7 y = 3 A(1, 7) B(9, 3) x y C(5, 5)

27. Midpoints Graph A(1, 1) and B(7, 9) 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.

28. Midpoints Graph A(1, 1) and B(7, 9) Check your answer using the midpoint formula. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.

29. Midpoints Graph A(1, 1) and B(7, 9) Check your answer using the midpoint formula. 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.

30. Midpoints Graph A(1, 1) and B(7, 9) C Check your answer using the midpoint formula. C(4, 5) 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Draw AB B(7, 9) A(1, 1) Estimate the midpoint of AB.

31. Midpoints 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

32. Midpoints B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

33. Midpoints x-coordinate of B y-coordinate of B B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

34. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

35. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

36. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 Add or subtract to isolate the variable B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) C(3, 5)

37. Midpoints x-coordinate of B y-coordinate of B Replace x 1 with 7 and y 1 with 2 Multiply each side by 2 Add or subtract to isolate the variable B(x, y) is somewhere over there. midpoint 0 y 0 x 10 -1 2 4 6 8 10 10 -1 2 4 6 8 10 -2 3 7 -2 1 5 9 1 9 3 -2 -2 5 7 Suppose C(3, 5) is the midpoint of AB. Find the coordinate of B. A(7, 2) B(-1, 8) C(3, 5)

38. Midpoints End of Lesson