Coordinate Geometry Worksheet for Maths Olympiad

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

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