Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 733 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
2. 2.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
4. 4.What is the midpoint of the line joining (1, 12) and (3, 6)? (a) (9, 2) (b) (4, 18) (c) (1, 3) (d) (2, 9)
5. 5.What is the midpoint of the line joining (8, 2) and (18, 6)? (a) (26, 8) (b) (13, 4) (c) (4, 13) (d) (5, 2)
6. 6.What is the midpoint of the line joining (1, 10) and (9, 12)? (a) (10, 22) (b) (4, 1) (c) (11, 5) (d) (5, 11)
7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
8. 8.In which quadrant does the point (−4, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
10. 10.What is the distance between the points (2, 5) and (14, 21)? (a) 21 (b) 400 (c) 28 (d) 20
11. 11.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
13. 13.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
14. 14.What is the midpoint of the line joining (0, 5) and (4, 9)? (a) (4, 14) (b) (7, 2) (c) (2, 2) (d) (2, 7)
15. 15.What is the midpoint of the line joining (3, 9) and (15, 17)? (a) (13, 9) (b) (9, 13) (c) (6, 4) (d) (18, 26)
16. 16.What is the distance between the points (8, 5) and (14, 13)? (a) 14 (b) 10 (c) 100 (d) 11
17. 17.What is the midpoint of the line joining (9, 9) and (15, 1)? (a) (3, 4) (b) (5, 12) (c) (24, 10) (d) (12, 5)
18. 18.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.In which quadrant does the point (8, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (2, 3) and (4, 13)? (a) (3, 8) (b) (8, 3) (c) (6, 16) (d) (1, 5)
21. 21.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
22. 22.What is the midpoint of the line joining (5, 10) and (17, 8)? (a) (9, 11) (b) (11, 9) (c) (22, 18) (d) (6, 1)
23. 23.What is the midpoint of the line joining (1, 9) and (3, 5)? (a) (2, 7) (b) (4, 14) (c) (1, 2) (d) (7, 2)
24. 24.In which quadrant does the point (8, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
25. 25.What is the distance between the points (3, 2) and (9, 10)? (a) 10 (b) 100 (c) 14 (d) 11
26. 26.What is the distance between the points (8, 4) and (15, 28)? (a) 625 (b) 26 (c) 25 (d) 31
27. 27.What is the midpoint of the line joining (7, 9) and (15, 17)? (a) (13, 11) (b) (22, 26) (c) (4, 4) (d) (11, 13)
28. 28.What is the midpoint of the line joining (10, 4) and (12, 14)? (a) (9, 11) (b) (22, 18) (c) (11, 9) (d) (1, 5)
29. 29.In which quadrant does the point (−2, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
30. 30.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.What is the midpoint of the line joining (1, 15) and (11, 3)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (5, 6)
32. 32.What is the distance between the points (4, 7) and (20, 19)? (a) 28 (b) 20 (c) 400 (d) 21
33. 33.What is the midpoint of the line joining (2, 4) and (6, 16)? (a) (8, 20) (b) (2, 6) (c) (10, 4) (d) (4, 10)
34. 34.What is the distance between the points (5, 25) and (12, 1)? (a) 31 (b) 26 (c) 25 (d) 625
35. 35.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
36. 36.What is the midpoint of the line joining (10, 8) and (18, 10)? (a) (4, 1) (b) (28, 18) (c) (14, 9) (d) (9, 14)
37. 37.What is the distance between the points (6, 0) and (18, 9)? (a) 15 (b) 225 (c) 16 (d) 21
38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
39. 39.What is the midpoint of the line joining (9, 2) and (21, 6)? (a) (4, 15) (b) (30, 8) (c) (6, 2) (d) (15, 4)
40. 40.What is the midpoint of the line joining (9, 9) and (15, 17)? (a) (13, 12) (b) (3, 4) (c) (24, 26) (d) (12, 13)

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