[discia] GCSE Maths › Geometry & Measures › Midpoint of a Line Segment

Midpoint of a Line Segment

discia.org 10 questions · 27 marks
Name Date
  1. Either paper 2 marks

    \(A\) is the point \((3, 7)\) and \(B\) is the point \((5, 11)\).

    Find the coordinates of the midpoint of \(AB\).

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    \((4, 9)\)
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  2. Either paper 1 mark

    The line segment \(AB\) is drawn on the grid.

    xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670AB

    Plot the midpoint of \(AB\) on the grid.

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    The midpoint is at \((0, 2)\)
    xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670ABM
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  3. Either paper 2 marks

    \(P\) has coordinates \((-15, 10)\) and \(Q\) has coordinates \((-1, -8)\).

    Work out the coordinates of the midpoint of \(PQ\).

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    \((-8, 1)\)
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  4. Either paper 2 marks

    The line segment \(ST\) is drawn on the grid.

    xy-8-7-6-5-4-3-212345678-8-7-6-5-4-3-2123456780ST

    Work out the coordinates of the midpoint of \(ST\).

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    \((-1, 3)\)
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  5. Either paper 2 marks

    \(A\) has coordinates \((-2, -6)\) and \(B\) has coordinates \((-3, -1)\).

    Calculate the coordinates of the midpoint of \(AB\).

    Give each coordinate as a decimal.

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    \((-2.5, -3.5)\)
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  6. Either paper 4 marks

    \(AB\) is a diameter of a circle.

    \(A\) has coordinates \((-4, 2)\) and \(B\) has coordinates \((12, -14)\).

    (a)

    Write down the coordinates of the centre of the circle.

    (b)

    \(PQ\) is a different diameter of the same circle.

    \(P\) has coordinates \((12, 2)\).

    Find the coordinates of \(Q\).

    Show answer
    (a) \((4, -6)\)
    (b) \((-4, -14)\)
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  7. Either paper 4 marks

    The triangle \(LMN\) is drawn on the grid.

    xy-9-8-7-6-5-4-3-2123456789-9-8-7-6-5-4-3-21234567890LMN
    (a)

    Work out the coordinates of the midpoint of \(LM\).

    (b)

    Work out the coordinates of the midpoint of \(MN\).

    Show answer
    (a) \((0, 5)\)
    (b) \((-2, -1)\)
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  8. Either paper 3 marks

    The grid is a map of a village. Each unit stands for 1 km.

    distance east (km)distance north (km)12345678910123456789100PoolMarket
    (a)

    State the coordinates of the Pool.

    (b)

    Reuben lives exactly halfway along the straight line from the Pool to the Market.

    Work out the coordinates of he house.

    Show answer
    (a) \((3, 5)\)
    (b) \((4, 4)\)
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  9. Either paper 4 marks

    The line \(AB\) is shown on the grid. \(A\) is the point \((2, -2)\) and \(B\) is the point \((-7, 4)\).

    xy-8-7-6-5-4-3-2-1123-4-3-2-1123450AB
    (a)

    Find the coordinates of the midpoint of \(AB\).

    (b)

    \(C\) is a point on \(AB\), not at \(A\) or \(B\). \(C\) is closer to \(A\) than to \(B\). The coordinates of \(C\) are whole numbers.

    Find the coordinates of \(C\).

    (c)

    On the grid, draw a line from the point \((-1, -3)\) that is parallel to \(AB\), runs in the same direction as \(A\) to \(B\), and is two thirds as long as \(AB\).

    Give the coordinates of the other end of your line.

    Show answer
    (a) \((-2.5, 1)\)
    (b) \((-1, 0)\)
    (c) \((-7, 1)\)
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  10. Either paper 3 marks

    Points \(E\), \(F\) and \(G\) are plotted on the grid.

    xy-10-8-6-4-2246810-10-9-8-7-6-5-4-3-2123456789100EFG
    (a)

    State the coordinates of \(G\).

    (b)

    State the coordinates of the midpoint of \(EG\).

    (c)

    The midpoint of \(EG\) is also the midpoint of \(FH\).

    Work out the coordinates of \(H\).

    Show answer
    (a) \((-4, -5)\)
    (b) \((-3, -3)\)
    (c) \((-7, 1)\)
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discia.org Midpoint of a Line Segment · sheet 1
Answers Midpoint of a Line Segment · sheet 1
  1. \((4, 9)\)
  2. The midpoint is at \((0, 2)\)
    xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670ABM
  3. \((-8, 1)\)
  4. \((-1, 3)\)
  5. \((-2.5, -3.5)\)
  6. (a) \((4, -6)\)
    (b) \((-4, -14)\)
  7. (a) \((0, 5)\)
    (b) \((-2, -1)\)
  8. (a) \((3, 5)\)
    (b) \((4, 4)\)
  9. (a) \((-2.5, 1)\)
    (b) \((-1, 0)\)
    (c) \((-7, 1)\)
  10. (a) \((-4, -5)\)
    (b) \((-3, -3)\)
    (c) \((-7, 1)\)
discia.org Midpoint of a Line Segment · sheet 1