Lesson 1.10f

1.10f Distance between points Quiz: OCR Maths, Unit 10

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.10f, Distance between points: 20 multiple choice questions for the OCR Maths (H240), Unit 10: Vectors, written with Revision Ninja.

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The 20 questions

  1. What is the distance between the points ai + bj and ci + dj?

    • (c - a)^2 + (d - b)^2
    • sqrt((c - a) + (d - b))
    • (c - a) + (d - b)
    • sqrt((c - a)^2 + (d - b)^2)

  2. What is the distance from the origin to the point (3, 4)?

    • 5
    • sqrt(7)
    • 7
    • 25

  3. The distance between two points is the magnitude of which vector quantity?

    • Their unit vector
    • Their position vector
    • Their displacement vector
    • Their sum vector

  4. Which theorem is used to calculate the distance between two points from vector components?

    • Binomial theorem
    • Sine rule
    • Cosine rule
    • Pythagoras' theorem

  5. What is the distance between a point and itself in a coordinate system?

    • 0
    • Undefined
    • Infinity
    • 1

  6. What is the distance formula between (x1, y1, z1) and (x2, y2, z2)?

    • sqrt((x2 - x1) + (y2 - y1) + (z2 - z1))
    • (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2
    • (x2 - x1) + (y2 - y1) + (z2 - z1)
    • sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

  7. What is the minimum possible value for the distance between two points?

    • -1
    • 1
    • Infinity
    • 0

  8. What is the distance between A(1, 2) and B(4, 6)?

    • 7
    • 5
    • sqrt(7)
    • 25

  9. What is the distance between A(-2, 3) and B(4, -5)?

    • sqrt(14)
    • 2
    • 14
    • 10

  10. Points P = 2i - 3j and Q = -i + 5j. What is the length PQ?

    • sqrt(55)
    • 11
    • sqrt(73)
    • sqrt(65)

  11. What is the distance between (1, 1) and (4, 7)?

    • sqrt(39)
    • 3 sqrt(7)
    • 9
    • 3 sqrt(5)

  12. What is the distance between A(1, 2, 3) and B(4, 6, 15)?

    • sqrt(160)
    • 5
    • 7
    • 13

  13. The point P(x, 0) is equidistant from A(1, 2) and B(5, 0). What is x?

    • x = 2.5
    • x = 2
    • x = 1.5
    • x = 3

  14. What type of triangle is formed by the vertices (0, 0), (3, 4), and (6, 0)?

    • Right-angled
    • Equilateral
    • Isosceles
    • Scalene

  15. A ship moves from (2, -1, 0) to (5, 3, 8) in km. What is the straight-line distance?

    • sqrt(41) km
    • sqrt(77) km
    • sqrt(89) km
    • 15 km

  16. What is the perimeter of the triangle with vertices A(0, 0), B(3, 0) and C(0, 4)?

    • 7
    • 10
    • 14
    • 12

  17. P = (k, 2) is distance sqrt(13) from A = (0, 0), with k > 0. What is k?

    • 3
    • sqrt(13)
    • 9
    • 4

  18. What is the distance from the origin to the midpoint of A(0, 0) and B(6, 8)?

    • 7
    • 10
    • sqrt(20)
    • 5

  19. A square has opposite vertices (0, 0) and (2, 2). What is the length of its diagonal?

    • 2 sqrt(2)
    • 8
    • sqrt(2)
    • 4

  20. P = (a, 2, -2) is distance 3 from the origin and a > 0. What is a?

    • sqrt(5)
    • 1
    • 2
    • 5

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