Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 401 · 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 distance between the points (7, 1) and (10, 5)? (a) 25 (b) 7 (c) 6 (d) 5
2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
3. 3.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.What is the midpoint of the line joining (4, 14) and (16, 6)? (a) (6, 4) (b) (20, 20) (c) (11, 10) (d) (10, 10)
5. 5.What is the midpoint of the line joining (0, 0) and (4, 10)? (a) (5, 2) (b) (2, 5) (c) (3, 5) (d) (4, 10)
6. 6.What is the midpoint of the line joining (0, 2) and (12, 0)? (a) (12, 2) (b) (7, 1) (c) (1, 6) (d) (6, 1)
7. 7.In which quadrant does the point (5, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
8. 8.In which quadrant does the point (5, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
10. 10.What is the midpoint of the line joining (7, 2) and (19, 12)? (a) (6, 5) (b) (13, 7) (c) (26, 14) (d) (7, 13)
11. 11.What is the distance between the points (2, 1) and (26, 8)? (a) 31 (b) 625 (c) 25 (d) 26
12. 12.What is the distance between the points (0, 0) and (3, 4)? (a) 25 (b) 7 (c) 6 (d) 5
13. 13.What is the distance between the points (0, 14) and (8, 8)? (a) 14 (b) 10 (c) 11 (d) 100
14. 14.What is the midpoint of the line joining (8, 8) and (14, 0)? (a) (11, 4) (b) (22, 8) (c) (4, 11) (d) (3, 4)
15. 15.What is the midpoint of the line joining (3, 10) and (11, 18)? (a) (14, 7) (b) (14, 28) (c) (7, 14) (d) (4, 4)
16. 16.What is the distance between the points (1, 19) and (9, 4)? (a) 23 (b) 289 (c) 18 (d) 17
17. 17.In which quadrant does the point (1, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
18. 18.What is the midpoint of the line joining (4, 10) and (14, 14)? (a) (5, 2) (b) (9, 12) (c) (12, 9) (d) (18, 24)
19. 19.What is the distance between the points (7, 17) and (19, 1)? (a) 400 (b) 20 (c) 21 (d) 28
20. 20.What is the distance between the points (4, 8) and (12, 23)? (a) 23 (b) 17 (c) 289 (d) 18
21. 21.What is the midpoint of the line joining (10, 16) and (14, 6)? (a) (11, 12) (b) (12, 11) (c) (2, 5) (d) (24, 22)
22. 22.What is the distance between the points (9, 1) and (17, 7)? (a) 14 (b) 100 (c) 11 (d) 10
23. 23.What is the midpoint of the line joining (3, 6) and (7, 12)? (a) (2, 3) (b) (10, 18) (c) (9, 5) (d) (5, 9)
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
25. 25.In which quadrant does the point (−2, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
26. 26.What is the distance between the points (1, 9) and (5, 12)? (a) 7 (b) 25 (c) 6 (d) 5
27. 27.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
28. 28.In which quadrant does the point (8, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (0, 9) and (24, 2)? (a) 31 (b) 625 (c) 26 (d) 25
30. 30.What is the distance between the points (6, 17) and (15, 5)? (a) 21 (b) 16 (c) 225 (d) 15
31. 31.What is the distance between the points (9, 0) and (15, 8)? (a) 10 (b) 100 (c) 14 (d) 11
32. 32.What is the distance between the points (3, 16) and (9, 8)? (a) 11 (b) 100 (c) 14 (d) 10
33. 33.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
34. 34.What is the distance between the points (6, 19) and (11, 7)? (a) 17 (b) 13 (c) 14 (d) 169
35. 35.What is the midpoint of the line joining (8, 5) and (18, 1)? (a) (13, 3) (b) (5, 2) (c) (26, 6) (d) (3, 13)
36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
37. 37.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
38. 38.What is the midpoint of the line joining (8, 5) and (14, 15)? (a) (11, 10) (b) (22, 20) (c) (3, 5) (d) (10, 11)
39. 39.What is the distance between the points (9, 24) and (21, 8)? (a) 21 (b) 20 (c) 400 (d) 28
40. 40.What is the distance between the points (1, 24) and (13, 8)? (a) 20 (b) 28 (c) 21 (d) 400

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