Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 347 · 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.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
3. 3.What is the midpoint of the line joining (7, 8) and (17, 16)? (a) (12, 12) (b) (24, 24) (c) (5, 4) (d) (13, 12)
4. 4.In which quadrant does the point (−5, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
6. 6.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
8. 8.What is the distance between the points (1, 6) and (17, 18)? (a) 400 (b) 20 (c) 28 (d) 21
9. 9.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
10. 10.What is the distance between the points (3, 3) and (11, 9)? (a) 10 (b) 100 (c) 14 (d) 11
11. 11.What is the distance between the points (7, 26) and (14, 2)? (a) 625 (b) 26 (c) 25 (d) 31
12. 12.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
13. 13.What is the distance between the points (2, 16) and (14, 0)? (a) 28 (b) 400 (c) 21 (d) 20
14. 14.What is the distance between the points (3, 18) and (15, 2)? (a) 20 (b) 28 (c) 400 (d) 21
15. 15.What is the distance between the points (9, 9) and (13, 12)? (a) 6 (b) 7 (c) 25 (d) 5
16. 16.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
17. 17.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (9, 8) and (15, 4)? (a) (3, 2) (b) (6, 12) (c) (12, 6) (d) (24, 12)
19. 19.What is the midpoint of the line joining (0, 14) and (8, 2)? (a) (8, 16) (b) (4, 6) (c) (4, 8) (d) (8, 4)
20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
21. 21.What is the distance between the points (5, 13) and (8, 9)? (a) 5 (b) 7 (c) 25 (d) 6
22. 22.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
24. 24.In which quadrant does the point (1, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
25. 25.What is the distance between the points (2, 9) and (26, 2)? (a) 31 (b) 625 (c) 25 (d) 26
26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
27. 27.What is the midpoint of the line joining (3, 9) and (7, 15)? (a) (2, 3) (b) (10, 24) (c) (5, 12) (d) (12, 5)
28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
29. 29.What is the distance between the points (9, 5) and (17, 20)? (a) 23 (b) 289 (c) 17 (d) 18
30. 30.What is the midpoint of the line joining (9, 0) and (13, 2)? (a) (22, 2) (b) (11, 1) (c) (2, 1) (d) (1, 11)
31. 31.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
33. 33.What is the midpoint of the line joining (2, 11) and (12, 5)? (a) (7, 8) (b) (5, 3) (c) (14, 16) (d) (8, 7)
34. 34.In which quadrant does the point (−8, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
35. 35.What is the midpoint of the line joining (7, 5) and (9, 1)? (a) (16, 6) (b) (8, 3) (c) (1, 2) (d) (3, 8)
36. 36.What is the midpoint of the line joining (7, 11) and (13, 1)? (a) (20, 12) (b) (3, 5) (c) (10, 6) (d) (6, 10)
37. 37.What is the distance between the points (7, 8) and (15, 23)? (a) 289 (b) 18 (c) 23 (d) 17
38. 38.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
39. 39.In which quadrant does the point (8, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (5, 12) and (7, 2)? (a) (12, 14) (b) (6, 7) (c) (1, 5) (d) (7, 6)

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