Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 532 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.What is the midpoint of the line joining (5, 12) and (13, 10)? (a) (4, 1) (b) (11, 9) (c) (9, 11) (d) (18, 22)
2. 2.What is the midpoint of the line joining (10, 4) and (18, 10)? (a) (28, 14) (b) (4, 3) (c) (7, 14) (d) (14, 7)
3. 3.What is the distance between the points (7, 16) and (22, 8)? (a) 289 (b) 18 (c) 23 (d) 17
4. 4.In which quadrant does the point (3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (4, 6) and (14, 18)? (a) (5, 6) (b) (12, 9) (c) (18, 24) (d) (9, 12)
6. 6.What is the midpoint of the line joining (4, 1) and (8, 7)? (a) (4, 6) (b) (2, 3) (c) (12, 8) (d) (6, 4)
7. 7.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
8. 8.What is the midpoint of the line joining (3, 4) and (9, 16)? (a) (6, 10) (b) (12, 20) (c) (3, 6) (d) (10, 6)
9. 9.What is the distance between the points (4, 6) and (7, 10)? (a) 6 (b) 25 (c) 5 (d) 7
10. 10.What is the midpoint of the line joining (0, 9) and (2, 15)? (a) (12, 1) (b) (2, 24) (c) (1, 3) (d) (1, 12)
11. 11.What is the distance between the points (2, 14) and (11, 2)? (a) 16 (b) 15 (c) 225 (d) 21
12. 12.What is the distance between the points (2, 9) and (17, 1)? (a) 18 (b) 23 (c) 289 (d) 17
13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
15. 15.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
16. 16.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
18. 18.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the distance between the points (8, 4) and (11, 8)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.What is the distance between the points (2, 6) and (9, 30)? (a) 625 (b) 31 (c) 25 (d) 26
21. 21.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.In which quadrant does the point (−7, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (6, 2) and (10, 14)? (a) (2, 6) (b) (9, 8) (c) (8, 8) (d) (16, 16)
24. 24.What is the distance between the points (8, 24) and (16, 9)? (a) 289 (b) 23 (c) 17 (d) 18
25. 25.What is the distance between the points (2, 17) and (14, 8)? (a) 21 (b) 225 (c) 15 (d) 16
26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
27. 27.What is the distance between the points (5, 2) and (9, 5)? (a) 7 (b) 5 (c) 6 (d) 25
28. 28.What is the midpoint of the line joining (5, 13) and (13, 7)? (a) (18, 20) (b) (10, 9) (c) (9, 10) (d) (4, 3)
29. 29.What is the distance between the points (6, 1) and (15, 13)? (a) 225 (b) 15 (c) 21 (d) 16
30. 30.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
32. 32.What is the midpoint of the line joining (6, 20) and (8, 8)? (a) (1, 6) (b) (14, 7) (c) (14, 28) (d) (7, 14)
33. 33.What is the midpoint of the line joining (2, 7) and (12, 17)? (a) (5, 5) (b) (14, 24) (c) (12, 7) (d) (7, 12)
34. 34.What is the midpoint of the line joining (6, 13) and (14, 1)? (a) (10, 7) (b) (7, 10) (c) (20, 14) (d) (4, 6)
35. 35.What is the distance between the points (5, 17) and (10, 5)? (a) 169 (b) 13 (c) 17 (d) 14
36. 36.What is the midpoint of the line joining (4, 0) and (6, 10)? (a) (10, 10) (b) (6, 5) (c) (5, 5) (d) (1, 5)
37. 37.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
38. 38.What is the midpoint of the line joining (1, 10) and (3, 8)? (a) (4, 18) (b) (2, 9) (c) (1, 1) (d) (9, 2)
39. 39.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
40. 40.What is the distance between the points (1, 9) and (7, 17)? (a) 100 (b) 11 (c) 14 (d) 10

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