Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 755 · 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, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
2. 2.What is the midpoint of the line joining (4, 7) and (6, 19)? (a) (5, 13) (b) (1, 6) (c) (13, 5) (d) (10, 26)
3. 3.What is the midpoint of the line joining (7, 0) and (19, 10)? (a) (26, 10) (b) (6, 5) (c) (13, 5) (d) (5, 13)
4. 4.What is the distance between the points (0, 4) and (12, 20)? (a) 20 (b) 400 (c) 28 (d) 21
5. 5.In which quadrant does the point (1, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (10, 4) and (12, 10)? (a) (22, 14) (b) (7, 11) (c) (11, 7) (d) (1, 3)
8. 8.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
9. 9.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
11. 11.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.What is the midpoint of the line joining (2, 9) and (8, 21)? (a) (10, 30) (b) (15, 5) (c) (3, 6) (d) (5, 15)
13. 13.What is the midpoint of the line joining (9, 9) and (11, 11)? (a) (10, 10) (b) (20, 20) (c) (1, 1) (d) (11, 10)
14. 14.What is the midpoint of the line joining (2, 19) and (4, 7)? (a) (6, 26) (b) (1, 6) (c) (13, 3) (d) (3, 13)
15. 15.In which quadrant does the point (8, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.What is the distance between the points (8, 20) and (20, 4)? (a) 400 (b) 28 (c) 21 (d) 20
17. 17.What is the distance between the points (1, 0) and (17, 12)? (a) 21 (b) 400 (c) 20 (d) 28
18. 18.What is the midpoint of the line joining (1, 8) and (5, 14)? (a) (11, 3) (b) (3, 11) (c) (2, 3) (d) (6, 22)
19. 19.What is the distance between the points (4, 14) and (9, 2)? (a) 17 (b) 14 (c) 13 (d) 169
20. 20.What is the midpoint of the line joining (1, 10) and (9, 8)? (a) (10, 18) (b) (9, 5) (c) (4, 1) (d) (5, 9)
21. 21.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
23. 23.In which quadrant does the point (7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
24. 24.In which quadrant does the point (9, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
26. 26.In which quadrant does the point (−8, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
27. 27.What is the midpoint of the line joining (5, 6) and (17, 14)? (a) (11, 10) (b) (10, 11) (c) (6, 4) (d) (22, 20)
28. 28.What is the distance between the points (9, 8) and (13, 5)? (a) 6 (b) 25 (c) 5 (d) 7
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
30. 30.What is the midpoint of the line joining (7, 5) and (17, 13)? (a) (5, 4) (b) (12, 9) (c) (24, 18) (d) (9, 12)
31. 31.In which quadrant does the point (−3, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
32. 32.What is the midpoint of the line joining (5, 13) and (17, 9)? (a) (6, 2) (b) (11, 11) (c) (22, 22) (d) (12, 11)
33. 33.What is the distance between the points (4, 8) and (8, 11)? (a) 6 (b) 25 (c) 5 (d) 7
34. 34.What is the distance between the points (5, 0) and (10, 12)? (a) 169 (b) 13 (c) 14 (d) 17
35. 35.What is the distance between the points (4, 17) and (9, 5)? (a) 17 (b) 14 (c) 169 (d) 13
36. 36.What is the distance between the points (3, 2) and (15, 11)? (a) 225 (b) 21 (c) 16 (d) 15
37. 37.What is the distance between the points (8, 9) and (14, 17)? (a) 10 (b) 14 (c) 11 (d) 100
38. 38.What is the midpoint of the line joining (0, 5) and (6, 9)? (a) (6, 14) (b) (3, 7) (c) (3, 2) (d) (7, 3)
39. 39.What is the distance between the points (6, 9) and (12, 17)? (a) 10 (b) 11 (c) 100 (d) 14
40. 40.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

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