Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 213 · 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.What is the distance between the points (2, 1) and (10, 7)? (a) 10 (b) 100 (c) 11 (d) 14
2. 2.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.What is the midpoint of the line joining (7, 11) and (15, 3)? (a) (7, 11) (b) (4, 4) (c) (22, 14) (d) (11, 7)
4. 4.What is the midpoint of the line joining (6, 7) and (10, 17)? (a) (2, 5) (b) (12, 8) (c) (8, 12) (d) (16, 24)
5. 5.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
9. 9.What is the midpoint of the line joining (6, 20) and (10, 10)? (a) (16, 30) (b) (8, 15) (c) (2, 5) (d) (15, 8)
10. 10.In which quadrant does the point (9, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
11. 11.What is the distance between the points (3, 0) and (11, 6)? (a) 100 (b) 14 (c) 11 (d) 10
12. 12.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
13. 13.What is the distance between the points (0, 6) and (7, 30)? (a) 25 (b) 26 (c) 625 (d) 31
14. 14.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
15. 15.What is the midpoint of the line joining (2, 6) and (4, 10)? (a) (1, 2) (b) (6, 16) (c) (3, 8) (d) (8, 3)
16. 16.What is the midpoint of the line joining (7, 13) and (19, 7)? (a) (13, 10) (b) (10, 13) (c) (6, 3) (d) (26, 20)
17. 17.In which quadrant does the point (−6, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
18. 18.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
21. 21.What is the distance between the points (1, 15) and (9, 9)? (a) 11 (b) 14 (c) 10 (d) 100
22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
23. 23.What is the midpoint of the line joining (1, 10) and (7, 6)? (a) (8, 4) (b) (3, 2) (c) (4, 8) (d) (8, 16)
24. 24.What is the distance between the points (3, 16) and (8, 4)? (a) 169 (b) 13 (c) 17 (d) 14
25. 25.What is the distance between the points (8, 5) and (16, 20)? (a) 289 (b) 18 (c) 17 (d) 23
26. 26.What is the distance between the points (8, 8) and (17, 20)? (a) 15 (b) 16 (c) 225 (d) 21
27. 27.What is the distance between the points (8, 6) and (20, 22)? (a) 400 (b) 28 (c) 20 (d) 21
28. 28.What is the midpoint of the line joining (2, 2) and (6, 14)? (a) (2, 6) (b) (4, 8) (c) (8, 4) (d) (8, 16)
29. 29.In which quadrant does the point (−7, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the midpoint of the line joining (9, 4) and (21, 0)? (a) (15, 2) (b) (2, 15) (c) (30, 4) (d) (6, 2)
31. 31.In which quadrant does the point (2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
32. 32.What is the midpoint of the line joining (5, 11) and (7, 9)? (a) (6, 10) (b) (10, 6) (c) (12, 20) (d) (1, 1)
33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
34. 34.What is the distance between the points (3, 16) and (12, 4)? (a) 16 (b) 21 (c) 225 (d) 15
35. 35.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (1, 5) and (5, 7)? (a) (2, 1) (b) (3, 6) (c) (6, 12) (d) (6, 3)
37. 37.What is the midpoint of the line joining (4, 9) and (14, 15)? (a) (12, 9) (b) (9, 12) (c) (18, 24) (d) (5, 3)
38. 38.What is the distance between the points (5, 9) and (14, 21)? (a) 16 (b) 21 (c) 225 (d) 15
39. 39.What is the distance between the points (0, 10) and (8, 4)? (a) 100 (b) 14 (c) 10 (d) 11
40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6

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