Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 130 · 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 (−2, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
5. 5.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
6. 6.What is the midpoint of the line joining (8, 3) and (18, 7)? (a) (13, 5) (b) (5, 13) (c) (5, 2) (d) (26, 10)
7. 7.What is the distance between the points (2, 0) and (26, 7)? (a) 31 (b) 26 (c) 25 (d) 625
8. 8.What is the midpoint of the line joining (2, 18) and (4, 6)? (a) (1, 6) (b) (6, 24) (c) (12, 3) (d) (3, 12)
9. 9.What is the midpoint of the line joining (0, 3) and (10, 1)? (a) (5, 2) (b) (5, 1) (c) (10, 4) (d) (2, 5)
10. 10.What is the distance between the points (1, 14) and (9, 8)? (a) 10 (b) 11 (c) 100 (d) 14
11. 11.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
12. 12.What is the midpoint of the line joining (3, 0) and (9, 12)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (3, 6)
13. 13.In which quadrant does the point (−6, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
15. 15.What is the distance between the points (5, 0) and (14, 12)? (a) 225 (b) 16 (c) 15 (d) 21
16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
17. 17.In which quadrant does the point (−5, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
19. 19.What is the distance between the points (5, 5) and (12, 29)? (a) 26 (b) 25 (c) 31 (d) 625
20. 20.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
22. 22.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
24. 24.What is the distance between the points (2, 5) and (9, 29)? (a) 26 (b) 25 (c) 31 (d) 625
25. 25.What is the distance between the points (0, 16) and (12, 0)? (a) 21 (b) 28 (c) 400 (d) 20
26. 26.What is the distance between the points (7, 9) and (13, 17)? (a) 14 (b) 11 (c) 100 (d) 10
27. 27.What is the midpoint of the line joining (3, 1) and (15, 7)? (a) (4, 9) (b) (18, 8) (c) (9, 4) (d) (6, 3)
28. 28.What is the distance between the points (6, 3) and (14, 9)? (a) 14 (b) 10 (c) 100 (d) 11
29. 29.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.What is the midpoint of the line joining (5, 4) and (11, 14)? (a) (9, 8) (b) (16, 18) (c) (8, 9) (d) (3, 5)
31. 31.In which quadrant does the point (−4, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the midpoint of the line joining (10, 15) and (14, 7)? (a) (11, 12) (b) (12, 11) (c) (2, 4) (d) (24, 22)
34. 34.What is the midpoint of the line joining (9, 14) and (13, 8)? (a) (2, 3) (b) (12, 11) (c) (22, 22) (d) (11, 11)
35. 35.In which quadrant does the point (−9, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
37. 37.What is the midpoint of the line joining (2, 9) and (12, 7)? (a) (8, 7) (b) (14, 16) (c) (7, 8) (d) (5, 1)
38. 38.What is the midpoint of the line joining (2, 13) and (10, 7)? (a) (4, 3) (b) (6, 10) (c) (12, 20) (d) (10, 6)
39. 39.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (0, 0) and (4, 2)? (a) (1, 2) (b) (4, 2) (c) (3, 1) (d) (2, 1)

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