Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 706 · 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 (5, 19) and (21, 7)? (a) 20 (b) 21 (c) 400 (d) 28
2. 2.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
3. 3.What is the distance between the points (9, 24) and (16, 0)? (a) 26 (b) 625 (c) 25 (d) 31
4. 4.In which quadrant does the point (−7, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
6. 6.What is the distance between the points (8, 1) and (15, 25)? (a) 625 (b) 26 (c) 31 (d) 25
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
9. 9.What is the distance between the points (0, 3) and (4, 0)? (a) 7 (b) 25 (c) 6 (d) 5
10. 10.What is the distance between the points (8, 0) and (15, 24)? (a) 26 (b) 25 (c) 31 (d) 625
11. 11.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the distance between the points (5, 8) and (17, 17)? (a) 225 (b) 16 (c) 15 (d) 21
13. 13.What is the midpoint of the line joining (2, 10) and (8, 14)? (a) (10, 24) (b) (12, 5) (c) (3, 2) (d) (5, 12)
14. 14.What is the midpoint of the line joining (2, 2) and (4, 8)? (a) (6, 10) (b) (5, 3) (c) (1, 3) (d) (3, 5)
15. 15.What is the midpoint of the line joining (10, 16) and (16, 4)? (a) (10, 13) (b) (26, 20) (c) (3, 6) (d) (13, 10)
16. 16.What is the midpoint of the line joining (0, 10) and (6, 12)? (a) (11, 3) (b) (3, 11) (c) (3, 1) (d) (6, 22)
17. 17.What is the midpoint of the line joining (1, 6) and (13, 18)? (a) (12, 7) (b) (14, 24) (c) (7, 12) (d) (6, 6)
18. 18.What is the distance between the points (9, 1) and (12, 5)? (a) 25 (b) 7 (c) 5 (d) 6
19. 19.What is the distance between the points (6, 1) and (11, 13)? (a) 17 (b) 14 (c) 13 (d) 169
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
21. 21.What is the distance between the points (1, 9) and (10, 21)? (a) 16 (b) 225 (c) 15 (d) 21
22. 22.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
23. 23.What is the midpoint of the line joining (7, 4) and (15, 6)? (a) (22, 10) (b) (5, 11) (c) (11, 5) (d) (4, 1)
24. 24.In which quadrant does the point (3, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
26. 26.What is the midpoint of the line joining (0, 21) and (4, 9)? (a) (2, 15) (b) (15, 2) (c) (4, 30) (d) (2, 6)
27. 27.What is the distance between the points (2, 6) and (10, 12)? (a) 10 (b) 11 (c) 14 (d) 100
28. 28.What is the midpoint of the line joining (2, 1) and (10, 11)? (a) (4, 5) (b) (12, 12) (c) (7, 6) (d) (6, 6)
29. 29.What is the distance between the points (8, 2) and (15, 26)? (a) 25 (b) 625 (c) 31 (d) 26
30. 30.What is the distance between the points (3, 15) and (8, 3)? (a) 13 (b) 14 (c) 169 (d) 17
31. 31.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
32. 32.What is the midpoint of the line joining (0, 3) and (2, 7)? (a) (5, 1) (b) (1, 5) (c) (1, 2) (d) (2, 10)
33. 33.What is the midpoint of the line joining (10, 8) and (18, 14)? (a) (28, 22) (b) (4, 3) (c) (14, 11) (d) (11, 14)
34. 34.What is the midpoint of the line joining (9, 4) and (15, 2)? (a) (24, 6) (b) (12, 3) (c) (3, 12) (d) (3, 1)
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
36. 36.What is the midpoint of the line joining (9, 2) and (15, 12)? (a) (7, 12) (b) (3, 5) (c) (24, 14) (d) (12, 7)
37. 37.What is the midpoint of the line joining (0, 6) and (10, 16)? (a) (10, 22) (b) (5, 5) (c) (11, 5) (d) (5, 11)
38. 38.In which quadrant does the point (−1, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
39. 39.What is the distance between the points (9, 0) and (21, 9)? (a) 225 (b) 15 (c) 21 (d) 16
40. 40.What is the midpoint of the line joining (2, 8) and (14, 2)? (a) (8, 5) (b) (16, 10) (c) (5, 8) (d) (6, 3)

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