Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 947 · 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 (1, 18) and (9, 6)? (a) (10, 24) (b) (5, 12) (c) (12, 5) (d) (4, 6)
2. 2.What is the distance between the points (2, 10) and (14, 5)? (a) 14 (b) 13 (c) 17 (d) 169
3. 3.What is the distance between the points (9, 6) and (21, 1)? (a) 17 (b) 14 (c) 169 (d) 13
4. 4.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
5. 5.What is the midpoint of the line joining (6, 4) and (12, 6)? (a) (3, 1) (b) (5, 9) (c) (18, 10) (d) (9, 5)
6. 6.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
7. 7.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
9. 9.What is the distance between the points (2, 3) and (5, 7)? (a) 6 (b) 7 (c) 5 (d) 25
10. 10.What is the distance between the points (7, 2) and (19, 7)? (a) 13 (b) 169 (c) 14 (d) 17
11. 11.In which quadrant does the point (−4, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
12. 12.What is the distance between the points (4, 3) and (13, 15)? (a) 16 (b) 225 (c) 21 (d) 15
13. 13.What is the midpoint of the line joining (10, 9) and (14, 13)? (a) (2, 2) (b) (24, 22) (c) (12, 11) (d) (11, 12)
14. 14.What is the distance between the points (2, 17) and (17, 9)? (a) 289 (b) 17 (c) 18 (d) 23
15. 15.What is the distance between the points (0, 2) and (12, 7)? (a) 169 (b) 17 (c) 13 (d) 14
16. 16.What is the midpoint of the line joining (0, 18) and (4, 10)? (a) (2, 4) (b) (2, 14) (c) (14, 2) (d) (4, 28)
17. 17.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.What is the distance between the points (2, 8) and (14, 17)? (a) 15 (b) 225 (c) 21 (d) 16
19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
21. 21.What is the midpoint of the line joining (0, 9) and (4, 11)? (a) (2, 10) (b) (4, 20) (c) (2, 1) (d) (10, 2)
22. 22.What is the distance between the points (0, 15) and (8, 0)? (a) 17 (b) 289 (c) 18 (d) 23
23. 23.What is the distance between the points (0, 8) and (9, 20)? (a) 16 (b) 225 (c) 15 (d) 21
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
25. 25.What is the distance between the points (9, 18) and (21, 9)? (a) 16 (b) 225 (c) 21 (d) 15
26. 26.What is the distance between the points (5, 15) and (21, 3)? (a) 400 (b) 20 (c) 28 (d) 21
27. 27.What is the distance between the points (0, 10) and (15, 2)? (a) 17 (b) 18 (c) 23 (d) 289
28. 28.What is the distance between the points (1, 0) and (9, 6)? (a) 10 (b) 100 (c) 14 (d) 11
29. 29.What is the distance between the points (9, 13) and (15, 5)? (a) 14 (b) 11 (c) 10 (d) 100
30. 30.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (0, 15) and (2, 3)? (a) (1, 6) (b) (1, 9) (c) (2, 18) (d) (9, 1)
32. 32.What is the distance between the points (5, 5) and (11, 13)? (a) 100 (b) 14 (c) 10 (d) 11
33. 33.In which quadrant does the point (4, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.What is the midpoint of the line joining (3, 19) and (5, 9)? (a) (8, 28) (b) (4, 14) (c) (1, 5) (d) (14, 4)
35. 35.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.In which quadrant does the point (7, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
37. 37.What is the midpoint of the line joining (7, 7) and (9, 19)? (a) (13, 8) (b) (1, 6) (c) (8, 13) (d) (16, 26)
38. 38.What is the distance between the points (5, 12) and (14, 0)? (a) 225 (b) 15 (c) 16 (d) 21
39. 39.What is the distance between the points (1, 16) and (9, 1)? (a) 18 (b) 289 (c) 23 (d) 17
40. 40.What is the midpoint of the line joining (4, 10) and (10, 0)? (a) (7, 5) (b) (3, 5) (c) (5, 7) (d) (14, 10)

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