Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 610 · 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 (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
2. 2.What is the distance between the points (1, 7) and (13, 2)? (a) 169 (b) 17 (c) 13 (d) 14
3. 3.In which quadrant does the point (−1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
4. 4.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
6. 6.What is the distance between the points (4, 0) and (16, 9)? (a) 15 (b) 16 (c) 225 (d) 21
7. 7.In which quadrant does the point (−2, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
8. 8.What is the midpoint of the line joining (10, 10) and (14, 22)? (a) (2, 6) (b) (16, 12) (c) (24, 32) (d) (12, 16)
9. 9.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
11. 11.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
12. 12.What is the distance between the points (4, 10) and (16, 5)? (a) 14 (b) 13 (c) 169 (d) 17
13. 13.What is the midpoint of the line joining (5, 7) and (11, 3)? (a) (3, 2) (b) (16, 10) (c) (8, 5) (d) (5, 8)
14. 14.What is the midpoint of the line joining (10, 5) and (12, 11)? (a) (22, 16) (b) (1, 3) (c) (8, 11) (d) (11, 8)
15. 15.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
16. 16.What is the distance between the points (5, 28) and (12, 4)? (a) 31 (b) 625 (c) 26 (d) 25
17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
18. 18.What is the distance between the points (2, 0) and (18, 12)? (a) 21 (b) 20 (c) 28 (d) 400
19. 19.What is the distance between the points (4, 6) and (16, 22)? (a) 20 (b) 21 (c) 28 (d) 400
20. 20.What is the distance between the points (1, 0) and (7, 8)? (a) 14 (b) 10 (c) 11 (d) 100
21. 21.In which quadrant does the point (3, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.In which quadrant does the point (7, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
25. 25.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
26. 26.What is the distance between the points (1, 8) and (9, 2)? (a) 100 (b) 11 (c) 10 (d) 14
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
28. 28.What is the distance between the points (4, 10) and (10, 2)? (a) 14 (b) 100 (c) 11 (d) 10
29. 29.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
30. 30.What is the midpoint of the line joining (4, 13) and (10, 1)? (a) (14, 14) (b) (7, 7) (c) (3, 6) (d) (8, 7)
31. 31.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
32. 32.What is the midpoint of the line joining (9, 7) and (13, 17)? (a) (12, 11) (b) (11, 12) (c) (22, 24) (d) (2, 5)
33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
34. 34.What is the midpoint of the line joining (7, 2) and (9, 12)? (a) (7, 8) (b) (16, 14) (c) (1, 5) (d) (8, 7)
35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
36. 36.What is the distance between the points (9, 16) and (21, 7)? (a) 225 (b) 16 (c) 15 (d) 21
37. 37.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
38. 38.What is the midpoint of the line joining (4, 9) and (14, 11)? (a) (5, 1) (b) (9, 10) (c) (10, 9) (d) (18, 20)
39. 39.In which quadrant does the point (2, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
40. 40.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

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