Coordinate geometry: past paper questions

Where the questions come from

• Question 8May/June 2026, paper 21Structured8 marks

  $P$ is the point $(0,4)$ and $Q$ is the point $(1,8)$. Find the coordinates of the midpoint of $PQ$.

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• Question 17Oct/Nov 2025, paper 22Structured11 marks

  $B$ is the point $(-3,1)$ and $D$ is the point $(-5,9)$. $BD$ is a diagonal of the kite $ABCD$. The ratio of the lengths of the diagonals $BD:AC=2:3$.

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• Question 22Oct/Nov 2024, paper 22Structured5 marks

  $A$ is the point $(17,9)$ and $B$ is the point $(23,39)$. Find the equation of the perpendicular bisector of line $AB$.

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• Question 17Oct/Nov 2023, paper 13Structured3 marksHas a diagram

  Find the equation of line $L$ in the form $y=mx+c$.

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• Question 12May/June 2026, paper 21Structured2 marks

  The coordinates of $A$ are $(3,20)$. The coordinates of $B$ are $(5,10)$. Work out the gradient of $AB$.

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• Question 22Oct/Nov 2025, paper 23Structured3 marks

  The equation of line $L$ is $y=-\frac{1}{2}x+7$. Find an equation of the line perpendicular to line $L$ that passes through the point $(3,5)$.

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• Question 2Oct/Nov 2024, paper 43Structured12 marksHas a diagram

  $A$ is the point $(3,7)$ and $B$ is the point $(-1,5)$. Find the coordinates of the midpoint of the line $AB$.

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• Question 12Oct/Nov 2023, paper 42Structured11 marksHas a diagram

  $O$ is the origin $(0,0)$, $A$ is the point $(8,1)$ and $B$ is the point $(2,5)$. Write as column vectors.

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• Question 12May/June 2026, paper 22Structured7 marks

  On the grid, draw these four straight lines.

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• Question 17Oct/Nov 2025, paper 41Structured3 marks

  Find the equation of the straight line that passes through the points $(2,0)$ and $(0,4)$.

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• Question 10Oct/Nov 2024, paper 43Structured11 marks

  The diagram shows a sketch of the graph of $y=3+2x-x^2$.

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• Question 9Oct/Nov 2023, paper 43Structured14 marks

  $A$ is the point $(0,2)$, $B$ is the point $(3,3)$ and $C$ is the point $(4,0)$. Determine if triangle $ABC$ is scalene, isosceles or equilateral.

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• Question 23May/June 2026, paper 22Structured7 marks

  The equation of a curve is $y=2x^2-11x+12$. Find the gradient of the tangent to the curve at $x=2$.

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• Question 6May/June 2025, paper 21Structured3 marks

  The line $x+y=7$ is drawn on the grid. On the grid, draw the line $y=2x+1$.

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• Question 1May/June 2024, paper 21Structured2 marksHas a diagram

  The diagram shows two sides of a parallelogram $ABCD$. Find the coordinates of point $D$.

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• Question 15May/June 2023, paper 22Structured7 marks

  $C$ is the point $(5,-1)$ and $D$ is the point $(13,15)$. Find the midpoint of $CD$.

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• Question 8May/June 2026, paper 23Structured4 marksHas a diagram

  The line $L$ is shown on the grid. Find the gradient of line $L$.

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• Question 11May/June 2025, paper 21Structured5 marksHas a diagram

  The diagram shows the graph of $y=\mathrm{f}(x)$ and the point $P(-2,11)$. The tangent from $P$ touches the graph of $y=\mathrm{f}(x)$ at the point $(a,b)$. The values of $a$ and $b$ are integers.

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• Question 11May/June 2024, paper 21Structured4 marksHas a diagram

  Find the inequalities that define the unshaded region, R. Find the inequalities that define the unshaded region, R.

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• Question 6May/June 2023, paper 41Structured14 marks

  In the square $ABCD$, $A$ has coordinates $(-2,1)$ and $B$ has coordinates $(1,5)$. $C$ has coordinates $(a,b)$, where $a$ and $b$ are both positive integers. Find the coordinates of $C$ and the coordinates of $D$.

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• Question 14May/June 2026, paper 43Structured7 marks

  $A$ is the point $(5,2)$ and $B$ is the point $(-3,6)$. Calculate the length of $AB$.

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• Question 24May/June 2025, paper 23Structured7 marks

  $A$ is the point $(a,12)$ and $B$ is the point $(b,27)$. Find the $y$-coordinate of the midpoint of $AB$.

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• Question 14May/June 2024, paper 22Structured2 marks

  $A$ is the point $(0,2)$ and $B$ is the point $(8,6)$. Find the equation of line $AB$.

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• Question 11May/June 2023, paper 43Structured9 marks

  $M$ has coordinates $(4,1)$ and $N$ has coordinates $(-2,-7)$. Find the length of $MN$.

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• Question 25May/June 2025, paper 42Structured5 marks

  $P$ is the point $(8,0)$ and $Q$ is the point $(20,6)$. Find the equation of the perpendicular bisector of $PQ$.

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• Question 10May/June 2024, paper 23Structured2 marks

  Find the gradient of the line joining the points $(-2,7)$ and $(3,1)$.

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• Question 13May/June 2025, paper 43Structured6 marks

  Line $L$ has the equation $y=2(x-5)$. Find the coordinates of the point where line $L$ intersects the $y$-axis.

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• Question 5May/June 2024, paper 41Structured17 marks

  $P$ is the point $(1,7)$. $Q$ is the point $(5,-5)$. Find $\overrightarrow{PQ}$.

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• Question 10May/June 2024, paper 42Structured12 marks

  $A$ is the point $(6,2)$ and $B$ is the point $(3,-4)$. Find the coordinates of the midpoint of $AB$.

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