Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 790 · 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 (1, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
2. 2.What is the midpoint of the line joining (8, 6) and (14, 14)? (a) (3, 4) (b) (22, 20) (c) (10, 11) (d) (11, 10)
3. 3.In which quadrant does the point (−4, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
4. 4.What is the midpoint of the line joining (0, 13) and (4, 9)? (a) (2, 11) (b) (11, 2) (c) (2, 2) (d) (4, 22)
5. 5.In which quadrant does the point (−7, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
6. 6.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.In which quadrant does the point (−5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
8. 8.What is the distance between the points (0, 2) and (4, 5)? (a) 7 (b) 25 (c) 6 (d) 5
9. 9.In which quadrant does the point (−7, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the midpoint of the line joining (6, 8) and (18, 16)? (a) (12, 12) (b) (6, 4) (c) (13, 12) (d) (24, 24)
11. 11.What is the midpoint of the line joining (9, 4) and (11, 14)? (a) (20, 18) (b) (9, 10) (c) (1, 5) (d) (10, 9)
12. 12.What is the distance between the points (7, 7) and (12, 19)? (a) 17 (b) 14 (c) 169 (d) 13
13. 13.What is the midpoint of the line joining (7, 14) and (13, 6)? (a) (11, 10) (b) (3, 4) (c) (10, 10) (d) (20, 20)
14. 14.What is the distance between the points (6, 0) and (22, 12)? (a) 21 (b) 400 (c) 28 (d) 20
15. 15.What is the midpoint of the line joining (10, 4) and (12, 0)? (a) (2, 11) (b) (11, 2) (c) (22, 4) (d) (1, 2)
16. 16.What is the distance between the points (1, 11) and (13, 2)? (a) 16 (b) 21 (c) 225 (d) 15
17. 17.What is the distance between the points (2, 15) and (8, 7)? (a) 100 (b) 11 (c) 14 (d) 10
18. 18.What is the distance between the points (8, 12) and (11, 8)? (a) 7 (b) 25 (c) 5 (d) 6
19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
20. 20.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
21. 21.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
22. 22.What is the midpoint of the line joining (9, 21) and (11, 9)? (a) (20, 30) (b) (1, 6) (c) (10, 15) (d) (15, 10)
23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
24. 24.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
26. 26.What is the distance between the points (1, 17) and (7, 9)? (a) 11 (b) 14 (c) 100 (d) 10
27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
28. 28.What is the distance between the points (4, 24) and (11, 0)? (a) 625 (b) 31 (c) 25 (d) 26
29. 29.What is the midpoint of the line joining (0, 14) and (12, 6)? (a) (10, 6) (b) (6, 4) (c) (12, 20) (d) (6, 10)
30. 30.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
31. 31.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (9, 4) and (17, 6)? (a) (13, 5) (b) (4, 1) (c) (26, 10) (d) (5, 13)
33. 33.What is the distance between the points (2, 4) and (14, 9)? (a) 169 (b) 13 (c) 17 (d) 14
34. 34.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the distance between the points (3, 7) and (9, 15)? (a) 100 (b) 14 (c) 10 (d) 11
36. 36.What is the midpoint of the line joining (5, 14) and (9, 4)? (a) (14, 18) (b) (9, 7) (c) (2, 5) (d) (7, 9)
37. 37.In which quadrant does the point (8, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.What is the distance between the points (9, 2) and (33, 9)? (a) 625 (b) 31 (c) 25 (d) 26
39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
40. 40.What is the midpoint of the line joining (9, 4) and (17, 14)? (a) (26, 18) (b) (4, 5) (c) (13, 9) (d) (9, 13)

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