Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 450 · 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.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
4. 4.What is the midpoint of the line joining (3, 4) and (15, 10)? (a) (6, 3) (b) (9, 7) (c) (18, 14) (d) (7, 9)
5. 5.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
7. 7.What is the distance between the points (8, 9) and (14, 17)? (a) 11 (b) 100 (c) 14 (d) 10
8. 8.What is the distance between the points (5, 4) and (29, 11)? (a) 26 (b) 625 (c) 31 (d) 25
9. 9.What is the midpoint of the line joining (9, 10) and (21, 0)? (a) (5, 15) (b) (30, 10) (c) (15, 5) (d) (6, 5)
10. 10.What is the distance between the points (3, 0) and (9, 8)? (a) 10 (b) 11 (c) 100 (d) 14
11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
13. 13.What is the midpoint of the line joining (5, 11) and (9, 3)? (a) (2, 4) (b) (7, 7) (c) (14, 14) (d) (8, 7)
14. 14.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
15. 15.What is the distance between the points (9, 7) and (15, 15)? (a) 10 (b) 11 (c) 14 (d) 100
16. 16.In which quadrant does the point (3, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
17. 17.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.In which quadrant does the point (−7, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
19. 19.What is the distance between the points (9, 11) and (15, 3)? (a) 10 (b) 11 (c) 100 (d) 14
20. 20.What is the midpoint of the line joining (5, 8) and (17, 14)? (a) (11, 11) (b) (12, 11) (c) (6, 3) (d) (22, 22)
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
22. 22.What is the midpoint of the line joining (6, 10) and (10, 8)? (a) (9, 8) (b) (8, 9) (c) (16, 18) (d) (2, 1)
23. 23.What is the distance between the points (0, 3) and (9, 15)? (a) 21 (b) 15 (c) 16 (d) 225
24. 24.What is the distance between the points (1, 2) and (13, 7)? (a) 17 (b) 169 (c) 13 (d) 14
25. 25.What is the distance between the points (0, 6) and (12, 15)? (a) 225 (b) 16 (c) 15 (d) 21
26. 26.In which quadrant does the point (−4, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
27. 27.What is the distance between the points (3, 9) and (12, 21)? (a) 16 (b) 15 (c) 225 (d) 21
28. 28.What is the midpoint of the line joining (9, 2) and (11, 0)? (a) (1, 10) (b) (10, 1) (c) (20, 2) (d) (1, 1)
29. 29.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
30. 30.What is the midpoint of the line joining (4, 1) and (8, 3)? (a) (2, 1) (b) (12, 4) (c) (2, 6) (d) (6, 2)
31. 31.What is the distance between the points (4, 8) and (12, 23)? (a) 289 (b) 18 (c) 23 (d) 17
32. 32.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
34. 34.In which quadrant does the point (−5, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (7, 10) and (9, 0)? (a) (16, 10) (b) (1, 5) (c) (5, 8) (d) (8, 5)
36. 36.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
37. 37.What is the distance between the points (3, 6) and (27, 13)? (a) 26 (b) 25 (c) 625 (d) 31
38. 38.What is the midpoint of the line joining (4, 8) and (10, 16)? (a) (14, 24) (b) (7, 12) (c) (12, 7) (d) (3, 4)
39. 39.In which quadrant does the point (6, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
40. 40.What is the distance between the points (6, 10) and (10, 7)? (a) 7 (b) 25 (c) 6 (d) 5

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