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# Midpoints (Geometry 2_5)

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Students find the midpoint of segments on the number line and the coordinate plane.

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### Midpoints (Geometry 2_5)

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