1. Midpoint of a Line Segment
10C
Bakyt & Bridgette & Miguel

2. Видео-бейне

3. Екі нүкте арақашықтығын табу формуласы:

5. Find the coordinates of the midpoint of a line segment
Objective
Find the coordinates of the midpoint of a line segment

6. Midpoint
Definition of midpoint is the point on the segment that divides it into two segments of equal length. -5 3

7. Midpoint
The coordinates of the midpoint, J, of line segment IK shown on the number line can be found as follows: 3 -5
The coordinate of the midpoint is -1.

8. The Mid-Point of a Line
In general, the coordinates of the mid-point of the line segment joining (x1, y1) and (x2, y2) are given by:
(x2, y2)
(x1, y1) x y
is the mean of the x-coordinates.
Talk through the generalization of the result for any two points (x1, y1) and (x2, y2). As for the generalization for the distance between two points, it doesn’t matter which point is called (x1, y1) and which point is called (x2, y2).
is the mean of the y-coordinates.

9. Example:
Use this activity to explore the mid-points of given line segments.
Establish that the x-coordinate of the mid-point will be half way between the x-coordinates of the end points. This is the mean of the x-coordinates of the end-points.
The y-coordinate of the mid-point will be half way between the y-coordinates of the end points. This is the mean of the y-coordinates of the end-points.

11. Task 1 : Find the mid-point of each line segment
A(3, 7); B(9, 4); C(x; y)=?
D(3, -5); E(6, -3); F(x; y)=?
M(-5, -2); N(-7, -6); K(x; y)=?
S(-3, 4); T(5, 4); U(x; y)=?
P(-3.5, 4.7); Q(7.5, 1.3); R(x; y)=?
O(2.5, -3.9); V(-8.7, 0.9); W(x; y)=?

12. ANSWERS: midpoint C(6; 5,5) midpoint F(4,5; -4) midpoint K(-6; -4)
midpoint U(1; 4)
midpoint R (2; 3)
midpoint W(-3,1; -1,5)

13. Task 2:
Physics real life problem.

14. An athlete runs along a circular path maintaining a constant speed of 7.85 m s–1. It takes him 16 seconds to complete one full circle. Find the average velocity after he completes 3/4 of the path.
x/ m
y/ m 20 40
Answer: 2.4 m s–1

15. Seesaw
Wavelength

16. Task 3: The endpoints of a diameter of a circle are (-1, 2) and (3, -3). Find the coordinates of the center of the circle.
The diameter of a circle is a line segment. The center of a circle is the midpoint of the diameter.

17. 1-желтоқсан Тұңғыш Президент күні
1-желтоқсан Тұңғыш Президент күні
Pyramid
Park first
President Nazarbayev
N.A.Nazarbayev
Khan-Shatyr
Nazarbayev IS of PM
in Aktobe

18. Task 4:
Find the midpoint of the following segments with the given points and draw the line segments:
1. (2; 5) and (8; 7)
2. (4; -6) and (6; 8)
3. (9; -4) and (-5; -4)
4. (-3; -5) and (3; 5)
(5; 6)
(5; 1)
(2;-4)
(0;0)

19. Экономикалық сызық ойыны
1. Екі нүктенің арақашықтығы - ең қысқа арақашықтық.
2. (-3; 3) және (3; -5) нүктелерін қосатын кесінді ортасының координасы (3; 4).
3. Түзудің екі нүктемен шектелген бөлігі кесінді деп аталады.
4. XoY координаталар жазықтығын енгізген
математик есімі - Л.Фиббоначчи

20. 5. Графигі (0; 0) нүктесіне қарағанда
симметриялы болатын функция – жұп
функция деп аталады.
6. Екі нүкте арақашықтығын есептеу формуласы:
7. Берілген кесіндіні тең екі бөлікке бөлетін
нүкте кесіндінің орта нүктесі деп аталады

21. Reflection: Today I learned ... It was difficult… I realized that ...
I was able to ...
It was interesting to know that ...
I was surprised ...
I wanted to ...