Length and midpoint: past paper questions

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• 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 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 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 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 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 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 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 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 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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• 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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