Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 156 · 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 (−2, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
2. 2.What is the distance between the points (0, 3) and (7, 27)? (a) 26 (b) 625 (c) 31 (d) 25
3. 3.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
6. 6.What is the distance between the points (6, 6) and (13, 30)? (a) 625 (b) 26 (c) 25 (d) 31
7. 7.What is the midpoint of the line joining (6, 11) and (16, 7)? (a) (11, 9) (b) (5, 2) (c) (22, 18) (d) (9, 11)
8. 8.What is the midpoint of the line joining (1, 1) and (7, 7)? (a) (3, 3) (b) (8, 8) (c) (5, 4) (d) (4, 4)
9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
10. 10.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
11. 11.What is the distance between the points (7, 1) and (14, 25)? (a) 26 (b) 31 (c) 625 (d) 25
12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
13. 13.What is the midpoint of the line joining (7, 2) and (17, 8)? (a) (5, 12) (b) (5, 3) (c) (24, 10) (d) (12, 5)
14. 14.In which quadrant does the point (−5, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
16. 16.What is the midpoint of the line joining (8, 0) and (18, 8)? (a) (5, 4) (b) (13, 4) (c) (4, 13) (d) (26, 8)
17. 17.What is the midpoint of the line joining (1, 9) and (9, 1)? (a) (4, 4) (b) (6, 5) (c) (5, 5) (d) (10, 10)
18. 18.What is the midpoint of the line joining (8, 8) and (18, 14)? (a) (13, 11) (b) (26, 22) (c) (5, 3) (d) (11, 13)
19. 19.What is the distance between the points (3, 1) and (10, 25)? (a) 26 (b) 25 (c) 31 (d) 625
20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
21. 21.In which quadrant does the point (9, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
23. 23.What is the distance between the points (0, 14) and (8, 8)? (a) 11 (b) 14 (c) 100 (d) 10
24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
25. 25.What is the distance between the points (6, 19) and (14, 4)? (a) 23 (b) 289 (c) 18 (d) 17
26. 26.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
27. 27.What is the distance between the points (0, 2) and (5, 14)? (a) 14 (b) 13 (c) 17 (d) 169
28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
29. 29.What is the distance between the points (3, 9) and (15, 25)? (a) 20 (b) 28 (c) 21 (d) 400
30. 30.What is the midpoint of the line joining (3, 10) and (9, 12)? (a) (12, 22) (b) (6, 11) (c) (3, 1) (d) (11, 6)
31. 31.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
32. 32.What is the midpoint of the line joining (3, 2) and (7, 4)? (a) (10, 6) (b) (2, 1) (c) (3, 5) (d) (5, 3)
33. 33.In which quadrant does the point (2, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
34. 34.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (3, 3) and (13, 13)? (a) (9, 8) (b) (8, 8) (c) (5, 5) (d) (16, 16)
36. 36.In which quadrant does the point (2, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
38. 38.What is the midpoint of the line joining (1, 20) and (9, 8)? (a) (10, 28) (b) (4, 6) (c) (5, 14) (d) (14, 5)
39. 39.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
40. 40.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

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