Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 59 · 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, 4) and (7, 16)? (a) 169 (b) 14 (c) 17 (d) 13
2. 2.What is the midpoint of the line joining (4, 9) and (14, 3)? (a) (9, 6) (b) (6, 9) (c) (5, 3) (d) (18, 12)
3. 3.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.In which quadrant does the point (−9, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
6. 6.What is the midpoint of the line joining (6, 3) and (8, 11)? (a) (1, 4) (b) (8, 7) (c) (14, 14) (d) (7, 7)
7. 7.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
8. 8.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 6 (c) 5 (d) 25
9. 9.What is the midpoint of the line joining (8, 3) and (12, 15)? (a) (20, 18) (b) (10, 9) (c) (9, 10) (d) (2, 6)
10. 10.In which quadrant does the point (−5, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
11. 11.What is the distance between the points (3, 1) and (11, 7)? (a) 100 (b) 14 (c) 11 (d) 10
12. 12.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the distance between the points (3, 3) and (15, 8)? (a) 14 (b) 13 (c) 17 (d) 169
14. 14.What is the distance between the points (1, 4) and (4, 0)? (a) 5 (b) 25 (c) 7 (d) 6
15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
16. 16.What is the midpoint of the line joining (0, 16) and (2, 4)? (a) (1, 6) (b) (1, 10) (c) (2, 20) (d) (10, 1)
17. 17.What is the distance between the points (6, 0) and (15, 12)? (a) 16 (b) 225 (c) 15 (d) 21
18. 18.What is the midpoint of the line joining (9, 12) and (17, 0)? (a) (26, 12) (b) (4, 6) (c) (13, 6) (d) (6, 13)
19. 19.What is the midpoint of the line joining (0, 10) and (10, 18)? (a) (10, 28) (b) (14, 5) (c) (5, 14) (d) (5, 4)
20. 20.What is the distance between the points (1, 7) and (9, 13)? (a) 14 (b) 100 (c) 11 (d) 10
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
23. 23.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
24. 24.What is the distance between the points (4, 2) and (10, 10)? (a) 10 (b) 100 (c) 11 (d) 14
25. 25.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
26. 26.What is the distance between the points (9, 17) and (14, 5)? (a) 13 (b) 17 (c) 169 (d) 14
27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
28. 28.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
29. 29.What is the midpoint of the line joining (9, 9) and (21, 1)? (a) (6, 4) (b) (30, 10) (c) (15, 5) (d) (5, 15)
30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
31. 31.What is the midpoint of the line joining (9, 8) and (21, 14)? (a) (11, 15) (b) (6, 3) (c) (30, 22) (d) (15, 11)
32. 32.What is the distance between the points (9, 31) and (16, 7)? (a) 25 (b) 31 (c) 625 (d) 26
33. 33.What is the distance between the points (8, 6) and (13, 18)? (a) 17 (b) 13 (c) 169 (d) 14
34. 34.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
35. 35.What is the distance between the points (1, 2) and (7, 10)? (a) 100 (b) 14 (c) 11 (d) 10
36. 36.What is the midpoint of the line joining (5, 18) and (9, 6)? (a) (14, 24) (b) (2, 6) (c) (7, 12) (d) (12, 7)
37. 37.What is the midpoint of the line joining (10, 3) and (14, 1)? (a) (24, 4) (b) (2, 1) (c) (2, 12) (d) (12, 2)
38. 38.What is the midpoint of the line joining (6, 18) and (10, 8)? (a) (13, 8) (b) (2, 5) (c) (8, 13) (d) (16, 26)
39. 39.In which quadrant does the point (−1, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26

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