[discia] GCSE Maths › Algebra › Coordinates

Coordinates

discia.org 10 questions · 25 marks
Name Date
  1. Either paper 3 marks

    The points \(D\), \(E\) and \(F\) are marked on the grid.

    xy-7-6-5-4-3-21234567-7-6-5-4-3-212345670DEF
    (a)

    State the coordinates of \(D\).

    (b)

    State the coordinates of \(E\).

    (c)

    State the coordinates of \(F\).

    Show answer
    (a) \((5, 4)\)
    (b) \((-3, 3)\)
    (c) \((-4, -2)\)
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  2. Either paper 2 marks

    Plot the points \(L\,(5, 2)\) and \(M\,(-3, -4)\) on the grid.

    xy-6-5-4-3-2123456-6-5-4-3-2-11234560
    Show answer
    \(L\) at \((5, 2)\) and \(M\) at \((-3, -4)\)
    xy-6-5-4-3-2123456-6-5-4-3-2-11234560LM
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  3. Either paper 4 marks

    Every point of a shape is moved 3 units to the right and 2 units down.

    (a)

    The point \(A\) has coordinates \((-6, -2)\).

    Write down the coordinates of the image of \(A\).

    (b)

    The image of the point \(B\) has coordinates \((-3, -5)\).

    Write down the coordinates of \(B\).

    Show answer
    (a) \((-3, -4)\)
    (b) \((-6, -3)\)
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  4. Either paper 2 marks

    \(A\) is the point \((6, 7)\) and \(B\) is the point \((10, 11)\).

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

    Show answer
    \((8, 9)\)
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  5. Either paper 2 marks

    Four points are marked on the grid.

    xy-6-5-4-3-2123456-6-5-4-3-2-11234560PQRS
    (a)

    Write down the coordinates of \(P\).

    (b)

    One of the points has coordinates \((-3, -5)\).

    Write down the letter of that point.

    Show answer
    (a) \((5, 2)\)
    (b) R
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  6. Either paper 1 mark

    \(PQRS\) is a rectangle. Three of its corners are marked on the grid.

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

    Plot the point \(S\) on the grid.

    Show answer
    \(S\) at \((-3, 1)\)
    xy-8-7-6-5-4-3-212345678-8-7-6-5-4-3-2123456780PQRS
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  7. Either paper 2 marks

    \(P\) is the point \((-5, -3)\).

    \(P\) is reflected in the \(x\)-axis to give the point \(P'\).

    Write down the coordinates of \(P'\).

    Show answer
    \((-5, 3)\)
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  8. Either paper 4 marks

    \(ABCD\) is a rectangle. Its sides are parallel to the axes.

    \(A\) is the point \((-3, 3)\) and \(C\) is the point \((5, 11)\).

    (a)

    \(B\) is the point \((5, 3)\).

    Write down the coordinates of \(D\).

    (b)

    Calculate the coordinates of the centre of the rectangle.

    Show answer
    (a) \((-3, 11)\)
    (b) \((1, 7)\)
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  9. Either paper 2 marks

    \(JKLM\) is a parallelogram.

    Three of its vertices are marked on the grid.

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

    Calculate the coordinates of \(M\).

    Show answer
    \((5, -1)\)
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  10. Either paper 3 marks

    Three points are marked on the grid.

    xy246810121416182024681012141618200STU
    (a)

    State the coordinates of \(S\).

    (b)

    State the coordinates of \(T\).

    (c)

    State the coordinates of \(U\).

    Show answer
    (a) \((6, 16)\)
    (b) \((1, 14)\)
    (c) \((9, 19)\)
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discia.org Coordinates · sheet 1
Answers Coordinates · sheet 1
  1. (a) \((5, 4)\)
    (b) \((-3, 3)\)
    (c) \((-4, -2)\)
  2. \(L\) at \((5, 2)\) and \(M\) at \((-3, -4)\)
    xy-6-5-4-3-2123456-6-5-4-3-2-11234560LM
  3. (a) \((-3, -4)\)
    (b) \((-6, -3)\)
  4. \((8, 9)\)
  5. (a) \((5, 2)\)
    (b) R
  6. \(S\) at \((-3, 1)\)
    xy-8-7-6-5-4-3-212345678-8-7-6-5-4-3-2123456780PQRS
  7. \((-5, 3)\)
  8. (a) \((-3, 11)\)
    (b) \((1, 7)\)
  9. \((5, -1)\)
  10. (a) \((6, 16)\)
    (b) \((1, 14)\)
    (c) \((9, 19)\)
discia.org Coordinates · sheet 1