Coordinate Geometry Worksheet for Maths Olympiad

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

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