c) P(1,-6) and Q(17,6)
d) R(7,-5) and U(-5,4)
3. Solve the following problems. Cartesian plane, a) AB is a straight line b) In a Cartesian PQ is a parallel to the on a Cartesian plane. x-axis. The distance Point B lies vertically between points P and Q below point A(3,6) is 4 units and the and the length of AB coordinates of Q are is 8 units. Find the (4,2). Find the coordinates of point B. coordinates of point P.
e) T(-2,7) and U(6,8)
c) Which of the points X(-3,8) and Y(5,-7) is closer to the origin? 3. Given that A( – 3,7) 3,7) and B( – 3,3), 3,3), find the midpoint of AB.
4. Find the coordinates of the midpoint of the points P( – 2,6) 2,6) and
Q(6,12).
5. Given that the points S( – 4,6) 4,6) and T(7,6), find the length of ST.
6. Given that the points L( – 5, 5, – 7) 7) and M( – 5,12), 5,12), find the length of LM.
8.4 Midpoint
7. The diagram shows a right-angled triangle, PQR. Given that the area of triangle PQR is 21 unit2 , find (a) the value of h, (b) the length of PR. Answer: a)
b)
Form 2 - Chapter 8 Coordinates Simple notes for this chapter. 8.1 Coordinates位置 1. Cartesian plane (直) y- axis
2. Plot and state coordinates. When do this, remember ( 先看X, 再看Y)
(X,Y) eg(5,-1) ***origin = (0,0) 8.2 Scales比例 for the Coordinates x-axis = 1:2 y-axis = 1:1
(横) x-axis
8.3 Distance between two points in a Cartesian plane straight just count the box or Pythagoras Theorem formula
8.4 Midpoint 中点
1. Formula of midpoint: Example of midpoint formula is shown above. Other practice for the subtopic distance between and and midpoint can try to do the left side or upside on this page. Do it in A4 Paper. Other exercise for the subtopic can try to do on the next page.
Midpoint Formula Worksheet 1. (5,0), (1,4)
4. (-6,-10), (-2,-8)
7. (5,10), (-3,6)
10. (-9,-4), (-3,6)
2. (-2,9), (-7,7)
5. (2,3), (4,-7)
8. (8,1), (-2,-5)
11. (2,5), (8,7)
19. (7,4), (9, -1)
20. (8,-9), (0,5)
21. (0,4), (-4,-12)
22. (-4,2), (2,-3)
23. (5,9), (-1,9)
24. (1,-7), (1,-12)
25. (-7,8), (-2, -9)
26. (14,0), (-7,5)
27. (14,-8), (12,-1)
28. (2,-11), (-9,0)
29. (-4,-6), (3,-6)
30. (4,-1), (2,-7)
Answer Key: 1. 4. 7. 10. 13. 16. 19. 22. 25. 28.
2. 5. 8. 11. 14. 17. 20. 23. 26. 29.
3. 6. 9. 12. 15. 18. 21. 24. 27. 30.
3. (-1,-6), (3,0)
6. (-9,3), (7,-8)
9. (4,-1), (-5,9)
12. (4,-6), (6,8)
13. (-3,0), (7,0)
14. (9,-4), (-5,-4)
15. (0,0), (11,9)
16. (-1,3), (-2,-11)
17. (10,14), (6,-6)
18. (-3,-5), (3,5)
