Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 356 · 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 (−5, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.What is the distance between the points (1, 9) and (5, 6)? (a) 25 (b) 5 (c) 6 (d) 7
3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
5. 5.What is the midpoint of the line joining (1, 8) and (5, 14)? (a) (11, 3) (b) (2, 3) (c) (6, 22) (d) (3, 11)
6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
8. 8.What is the midpoint of the line joining (10, 1) and (16, 7)? (a) (26, 8) (b) (3, 3) (c) (4, 13) (d) (13, 4)
9. 9.What is the distance between the points (9, 9) and (24, 1)? (a) 289 (b) 23 (c) 17 (d) 18
10. 10.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
11. 11.What is the distance between the points (8, 3) and (17, 15)? (a) 16 (b) 21 (c) 225 (d) 15
12. 12.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (1, 13) and (5, 5)? (a) (3, 9) (b) (9, 3) (c) (6, 18) (d) (2, 4)
14. 14.What is the distance between the points (9, 0) and (13, 3)? (a) 25 (b) 6 (c) 5 (d) 7
15. 15.In which quadrant does the point (−6, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
16. 16.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
17. 17.What is the distance between the points (7, 15) and (16, 3)? (a) 15 (b) 16 (c) 225 (d) 21
18. 18.What is the midpoint of the line joining (2, 9) and (12, 17)? (a) (5, 4) (b) (14, 26) (c) (13, 7) (d) (7, 13)
19. 19.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
20. 20.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
21. 21.What is the distance between the points (3, 0) and (27, 7)? (a) 25 (b) 31 (c) 26 (d) 625
22. 22.What is the distance between the points (6, 16) and (12, 8)? (a) 14 (b) 11 (c) 100 (d) 10
23. 23.In which quadrant does the point (−3, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
24. 24.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
25. 25.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (2, 13) and (14, 8)? (a) 17 (b) 169 (c) 13 (d) 14
27. 27.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (3, 1) and (6, 5)? (a) 7 (b) 25 (c) 6 (d) 5
29. 29.What is the midpoint of the line joining (8, 10) and (12, 20)? (a) (20, 30) (b) (2, 5) (c) (10, 15) (d) (15, 10)
30. 30.What is the distance between the points (1, 29) and (8, 5)? (a) 25 (b) 31 (c) 625 (d) 26
31. 31.What is the distance between the points (2, 1) and (14, 6)? (a) 14 (b) 13 (c) 17 (d) 169
32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
33. 33.What is the midpoint of the line joining (8, 9) and (14, 13)? (a) (12, 11) (b) (11, 11) (c) (3, 2) (d) (22, 22)
34. 34.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.What is the midpoint of the line joining (4, 14) and (16, 6)? (a) (20, 20) (b) (11, 10) (c) (6, 4) (d) (10, 10)
37. 37.In which quadrant does the point (−2, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
38. 38.What is the distance between the points (2, 12) and (10, 6)? (a) 14 (b) 11 (c) 10 (d) 100
39. 39.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
40. 40.What is the distance between the points (9, 1) and (21, 6)? (a) 169 (b) 14 (c) 17 (d) 13

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