Perpendicular lines: past paper questions

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• Question 15May/June 2026, paper 12Structured8 marks

  The equation of line $L$ is $2y+x=19$. Find the gradient of line $L$.

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• Question 24Oct/Nov 2024, paper 12Structured5 marks

  $P$ is the point $(-1,4)$ and $Q$ is the point $(-3,-2)$. Find the coordinates of the midpoint of the line $PQ$.

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• Question 7Oct/Nov 2023, paper 22Structured10 marksHas a diagram

  Point $A$ and point $B$ are shown on a centimetre square grid. $ABC$ is a triangle. Here are five possible coordinates for point $C$.

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• Question 18Oct/Nov 2025, paper 22Structured9 marksHas a diagram

  The equation of line $L$ is $y=\frac{x}{5}+3$. Write down the gradient of line $L$.

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• Question 7Oct/Nov 2024, paper 21Structured10 marks

  $ABCD$ is a parallelogram with sides $AB$, $BC$, $CD$ and $DA$. $A$ is the point $(-3,7)$ and $B$ is the point $(2,5)$. $\overrightarrow{AD}=\left(\begin{array}{c}-1\\ -6\end{array}\right)$ Find the coordinates of point $D$.

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• Question 26May/June 2023, paper 11Structured5 marks

  $A$ is the point $(-2,3)$ and $B$ is the point $(4,7)$. Find the coordinates of the midpoint of $AB$.

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• Question 17May/June 2025, paper 12Structured5 marks

  The equation of line L is $5y+3x=10$. Rearrange $5y+3x=10$ to make $y$ the subject.

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• Question 23May/June 2024, paper 11Structured7 marks

  $AB$ is a line segment joining $A(-2,5)$ and $B(1,3)$. $B$ is the midpoint of the line segment $AC$. Find the coordinates of $C$.

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• Question 24May/June 2023, paper 12Structured5 marks

  $A$ is the point $(3,11)$ and $B$ is the point $(-5,-5)$. The equation of line $L$ is $2y+x=5$. Show that line $L$ is the perpendicular bisector of $AB$.

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• Question 11May/June 2024, paper 22Structured10 marks

  $Q$ is the point $(n,-4)$, $R$ is the point $(-1,8)$ and $S$ is the point $(3,2)$. The length $QR$ is 13 units. Find the two possible values of $n$.

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