Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 294 · 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 (7, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (6, 2) and (14, 14)? (a) (4, 6) (b) (10, 8) (c) (20, 16) (d) (8, 10)
3. 3.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
5. 5.What is the distance between the points (2, 3) and (5, 7)? (a) 25 (b) 7 (c) 6 (d) 5
6. 6.What is the midpoint of the line joining (2, 9) and (10, 11)? (a) (10, 6) (b) (12, 20) (c) (4, 1) (d) (6, 10)
7. 7.What is the distance between the points (3, 18) and (12, 6)? (a) 225 (b) 15 (c) 21 (d) 16
8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
9. 9.What is the midpoint of the line joining (10, 4) and (12, 16)? (a) (11, 10) (b) (22, 20) (c) (10, 11) (d) (1, 6)
10. 10.What is the distance between the points (4, 6) and (7, 10)? (a) 25 (b) 7 (c) 6 (d) 5
11. 11.What is the midpoint of the line joining (3, 4) and (13, 14)? (a) (5, 5) (b) (8, 9) (c) (16, 18) (d) (9, 8)
12. 12.What is the distance between the points (1, 2) and (8, 26)? (a) 25 (b) 26 (c) 31 (d) 625
13. 13.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
15. 15.What is the midpoint of the line joining (2, 8) and (10, 0)? (a) (4, 4) (b) (12, 8) (c) (4, 6) (d) (6, 4)
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
17. 17.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (8, 0) and (18, 10)? (a) (5, 13) (b) (5, 5) (c) (26, 10) (d) (13, 5)
19. 19.What is the midpoint of the line joining (2, 3) and (14, 1)? (a) (6, 1) (b) (2, 8) (c) (16, 4) (d) (8, 2)
20. 20.What is the midpoint of the line joining (2, 13) and (12, 1)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (5, 6)
21. 21.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
22. 22.What is the midpoint of the line joining (5, 7) and (11, 15)? (a) (16, 22) (b) (3, 4) (c) (8, 11) (d) (11, 8)
23. 23.In which quadrant does the point (7, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
24. 24.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.What is the distance between the points (2, 2) and (8, 10)? (a) 14 (b) 10 (c) 100 (d) 11
26. 26.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
27. 27.What is the distance between the points (1, 2) and (13, 11)? (a) 21 (b) 225 (c) 16 (d) 15
28. 28.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
29. 29.What is the midpoint of the line joining (8, 13) and (12, 1)? (a) (20, 14) (b) (2, 6) (c) (7, 10) (d) (10, 7)
30. 30.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
32. 32.In which quadrant does the point (6, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
34. 34.What is the midpoint of the line joining (10, 14) and (12, 10)? (a) (11, 12) (b) (22, 24) (c) (1, 2) (d) (12, 11)
35. 35.In which quadrant does the point (4, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (9, 18) and (13, 8)? (a) (13, 11) (b) (22, 26) (c) (2, 5) (d) (11, 13)
37. 37.What is the midpoint of the line joining (8, 0) and (10, 8)? (a) (1, 4) (b) (9, 4) (c) (4, 9) (d) (18, 8)
38. 38.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
39. 39.In which quadrant does the point (−6, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25

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