Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 161 · 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 (7, 4) and (11, 10)? (a) (9, 7) (b) (18, 14) (c) (2, 3) (d) (7, 9)
2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
5. 5.What is the distance between the points (5, 8) and (13, 2)? (a) 14 (b) 11 (c) 10 (d) 100
6. 6.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
7. 7.What is the distance between the points (3, 18) and (15, 2)? (a) 400 (b) 20 (c) 28 (d) 21
8. 8.What is the midpoint of the line joining (7, 3) and (17, 7)? (a) (12, 5) (b) (5, 2) (c) (24, 10) (d) (5, 12)
9. 9.What is the midpoint of the line joining (9, 19) and (11, 7)? (a) (13, 10) (b) (1, 6) (c) (20, 26) (d) (10, 13)
10. 10.What is the distance between the points (5, 8) and (8, 4)? (a) 5 (b) 6 (c) 25 (d) 7
11. 11.What is the distance between the points (3, 4) and (11, 19)? (a) 18 (b) 23 (c) 289 (d) 17
12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
13. 13.In which quadrant does the point (−9, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
14. 14.What is the midpoint of the line joining (10, 20) and (18, 8)? (a) (28, 28) (b) (4, 6) (c) (15, 14) (d) (14, 14)
15. 15.What is the midpoint of the line joining (3, 1) and (13, 5)? (a) (5, 2) (b) (16, 6) (c) (8, 3) (d) (3, 8)
16. 16.What is the midpoint of the line joining (7, 13) and (13, 7)? (a) (10, 10) (b) (11, 10) (c) (3, 3) (d) (20, 20)
17. 17.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
18. 18.What is the distance between the points (3, 12) and (12, 0)? (a) 16 (b) 225 (c) 15 (d) 21
19. 19.What is the midpoint of the line joining (1, 3) and (11, 7)? (a) (12, 10) (b) (5, 6) (c) (5, 2) (d) (6, 5)
20. 20.In which quadrant does the point (9, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
21. 21.What is the midpoint of the line joining (4, 10) and (10, 6)? (a) (3, 2) (b) (14, 16) (c) (8, 7) (d) (7, 8)
22. 22.What is the distance between the points (6, 13) and (18, 8)? (a) 169 (b) 17 (c) 14 (d) 13
23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
24. 24.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
26. 26.What is the midpoint of the line joining (7, 17) and (17, 5)? (a) (5, 6) (b) (12, 11) (c) (11, 12) (d) (24, 22)
27. 27.What is the distance between the points (4, 1) and (16, 10)? (a) 21 (b) 225 (c) 16 (d) 15
28. 28.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
29. 29.What is the distance between the points (2, 12) and (14, 3)? (a) 16 (b) 15 (c) 225 (d) 21
30. 30.What is the midpoint of the line joining (1, 5) and (5, 13)? (a) (2, 4) (b) (9, 3) (c) (3, 9) (d) (6, 18)
31. 31.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
32. 32.What is the midpoint of the line joining (2, 3) and (4, 11)? (a) (1, 4) (b) (3, 7) (c) (6, 14) (d) (7, 3)
33. 33.What is the midpoint of the line joining (1, 12) and (3, 8)? (a) (4, 20) (b) (10, 2) (c) (2, 10) (d) (1, 2)
34. 34.What is the distance between the points (6, 16) and (14, 1)? (a) 289 (b) 17 (c) 18 (d) 23
35. 35.What is the midpoint of the line joining (7, 3) and (9, 15)? (a) (9, 8) (b) (1, 6) (c) (16, 18) (d) (8, 9)
36. 36.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the midpoint of the line joining (5, 8) and (15, 16)? (a) (10, 12) (b) (12, 10) (c) (20, 24) (d) (5, 4)
38. 38.What is the midpoint of the line joining (0, 2) and (4, 10)? (a) (6, 2) (b) (4, 12) (c) (2, 4) (d) (2, 6)
39. 39.What is the distance between the points (6, 5) and (18, 14)? (a) 16 (b) 21 (c) 15 (d) 225
40. 40.What is the midpoint of the line joining (5, 10) and (17, 16)? (a) (6, 3) (b) (13, 11) (c) (22, 26) (d) (11, 13)

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