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Math 9 · Unit 13: Position and transformation · Cambridge Lower Secondary Maths Stage 9

13.2 Points on a line segment

28 questions · e.g. The point 3/5 of the way along OG

Practice

Questions

  1. 1. O is (0, 0) and A is (3, 6). What are the coordinates of the point 1/3 of the way along OA?

    xy12345612340A
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  2. 2. O is (0, 0) and A is (3, 6). What are the coordinates of the point 2/3 of the way along OA?

    xy12345612340A
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  3. 3. O is (0, 0) and B is (4, 12). What are the coordinates of the point 1/4 of the way along OB?

    xy123456789101112123450B
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  4. 4. O is (0, 0) and B is (4, 12). What is the point 3/4 of the way along OB?

    xy123456789101112123450B
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  5. 5. The line segment OC goes from O (0, 0) to C (24, 24). Match each fraction of the way along OC to its point. (1/8 of the way along OC is (3, 3).)

    xy2244668810101212141416161818202022222424CO
    • 1/4
    • 3/4
    • 1/2
    • 5/8
    • 3/8
    • (15, 15)
    • (6, 6)
    • (9, 9)
    • (18, 18)
    • (12, 12)
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  6. 6. Points A (3, 4), B (6, 8), C, … are equally spaced along a straight line from O. What are the coordinates of C?

    xy1234567891011121234567890AB
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  7. 7. Points A and B are equally spaced along a straight line from O, and the points continue along the line, each labelled with a letter in order from A. Complete the x- and y-coordinates of C, E and K in the table.

    LetterABCEKPosition in alphabet1st2nd3rd5th11thx-coordinate1 × 3 = 32 × 3 = 6y-coordinate1 × 4 = 42 × 4 = 8

    Fill the blanks with these.

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  8. 8. Points A (3, 4) and B (6, 8) are equally spaced along a straight line from O. The letters continue along the line in order. Which completes the statements? The x-coordinates are in the first number's times table and the y-coordinates in the second number's times table. To find a letter's coordinates, multiply its position in the alphabet by the first number for x and by the second number for y.

    xy1234567891011121234567890AB
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  9. 9. O is (0, 0) and G is (20, 25). What is the point 1/5 of the way along OG?

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  10. 10. O is (0, 0) and G is (20, 25). What is the point 3/5 of the way along OG?

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  11. 11. O is (0, 0) and H is (18, 12). What is the point 1/6 of the way along OH?

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  12. 12. O is (0, 0) and H is (18, 12). What is the point 5/6 of the way along OH?

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  13. 13. O is (0, 0) and A is (5, 8). Points A and B are equally spaced along the same line, so the distance OA equals the distance AB. What are the coordinates of B?

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  14. 14. O is (0, 0), A is (5, 8) and B is (10, 16), equally spaced along a line. C is the next point along the line, with BC equal to OA and AB. What are the coordinates of C?

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  15. 15. O is (0, 0) and A is (5, 8). The points continue along the line, equally spaced, each labelled with a letter in order from A. Which working shows that E, the 5th letter, is (25, 40)?

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  16. 16. O is (0, 0) and A is (5, 8). Points A, B, C, … are equally spaced along the line. Where is T, the 20th letter?

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  17. 17. O is (0, 0) and A is (5, 8). Points A, B, C, … are equally spaced along the line, each labelled with a letter in order. Which is the expression for the coordinates of the nth letter?

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  18. 18. O is (0, 0) and J is (42, 54). E, F, G, H and I are equally spaced between them. Where is H?

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  19. 19. C is (1, 1) and D is (10, 13). What is the point 1/3 of the way along CD?

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  20. 20. F is the point (2, 3) and G is the point (7, 18). H lies 2/5 of the way along FG. What are the coordinates of H?

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