Coordinates

Calculate $\begin{pmatrix}3\\-2\end{pmatrix} + \begin{pmatrix}1\\-1\end{pmatrix}$.

Feb/March 2017

The vectors given are $\mathbf{e} = \begin{pmatrix}-5\\4\end{pmatrix}$ and $\mathbf{f} = \begin{pmatrix}0\\6\end{pmatrix}$.

Feb/March 2019

Point A is at $(6,4)$, while point B is at $(2,7)$.

Feb/March 2020

Work out the value of $2 \begin{pmatrix}-3\\7\end{pmatrix}$.

Feb/March 2021

Let $\mathbf{v}=\begin{pmatrix}-1\\3\end{pmatrix}$ and $\mathbf{y}=\begin{pmatrix}2\\5\end{pmatrix}$.

Feb/March 2023

A coordinate grid is displayed, with point $A$ positioned at about $(7, 1)$ and point $B$ positioned at about $(-3, 4)$.

Feb/March 2024

Take $\mathbf{a} = \begin{pmatrix}3\\5\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}-8\\7\end{pmatrix}$.

May/June 2015

The coordinate grid displays two points, $A$ and $B$.

May/June 2015

A coordinate grid is displayed, and points $A$ and $B$ are marked on it. The axes are named $x$ and $y$.

May/June 2015

Calculate $PQ$.

May/June 2015

Calculate $\begin{pmatrix}-2\\-3\end{pmatrix} + \begin{pmatrix}-4\\7\end{pmatrix}$.

May/June 2016

Let $p = \begin{pmatrix}4\\-2\end{pmatrix}$ and $q = \begin{pmatrix}-3\\0\end{pmatrix}$.

May/June 2016

Express $3\begin{pmatrix}-2 \\ 1\end{pmatrix}$ as one vector.

May/June 2016

A dashed diagonal line is drawn on a coordinate grid from $(0,0)$ to $(5,5)$. A dashed horizontal line appears at $y=4$, while a solid horizontal line is shown at $y=3$. The shaded area is $R$.

May/June 2016

The diagram depicts a curve whose equation is $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$.

May/June 2016

$\mathbf{a} = \begin{pmatrix}5\\-1\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}-3\\-4\end{pmatrix}$.

May/June 2017

Let $g = \begin{pmatrix}2\\5\end{pmatrix}$ and $h = \begin{pmatrix}-3\\4\end{pmatrix}$.

May/June 2018

$a=\begin{pmatrix}5 \\ -2\end{pmatrix},\;b=\begin{pmatrix}-7 \\ -3\end{pmatrix}$

May/June 2018

Calculate \begin{pmatrix}5\\-1\end{pmatrix} + \begin{pmatrix}2\\6\end{pmatrix}.

May/June 2018

Find $\begin{pmatrix}4\\-2\end{pmatrix} - \begin{pmatrix}1\\5\end{pmatrix}$.

May/June 2019

The vectors are $p = \begin{pmatrix}5\\0\end{pmatrix}$ together with $q = \begin{pmatrix}1\\6\end{pmatrix}$.

May/June 2019

Calculate $\begin{pmatrix}6\\-5\end{pmatrix}+\begin{pmatrix}8\\-1\end{pmatrix}$.

May/June 2021

The vectors are given as $\mathbf{a} = \begin{pmatrix}5\\-7\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}-2\\6\end{pmatrix}$.

May/June 2021

The vectors are given by $\mathbf{a} = \begin{pmatrix}3 \\ -4\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}5 \\ 2\end{pmatrix}$.

May/June 2021

$\mathbf{p} = \begin{pmatrix}2\\8\end{pmatrix}$ while $\mathbf{q} = \begin{pmatrix}-1\\4\end{pmatrix}$

May/June 2022

The diagram displays point P and point R on a coordinate grid whose x- and y-axes are labelled.

May/June 2022

$a = \begin{pmatrix}3\\7\end{pmatrix}$ while $b = \begin{pmatrix}-2\\5\end{pmatrix}$.

May/June 2023

$F$ has coordinates $(1, -4)$, $\vec{FG} = \begin{pmatrix} 8 \\ -3 \end{pmatrix}$ and $\vec{GH} = \begin{pmatrix} -12 \\ 35 \end{pmatrix}$.

May/June 2023

The diagram plots two sides of parallelogram ABCD on a coordinate grid, with point A located at about $(-7,5)$, point B at $(-1,1)$ and point C at $(3,3)$.

May/June 2024

The vectors are defined by $\mathbf{a} = \begin{pmatrix}5\\-7\end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix}6\\-7\end{pmatrix}$.

May/June 2024

The diagram illustrates two edges of a parallelogram $ABCD$.

May/June 2024

The vectors are $p = \begin{pmatrix}4 \\ -2\end{pmatrix}$ and $q = \begin{pmatrix}-1 \\ 3\end{pmatrix}$.

Oct/Nov 2015

Express $\vec{AB}$ in column-vector form.

Oct/Nov 2015

The diagram displays a coordinate grid with points $A$ and $B$ marked on it. The axes are named $x$ and $y$.

Oct/Nov 2016

With $m = \begin{pmatrix} 5 \\ -7 \end{pmatrix}$ and $n = \begin{pmatrix} 2 \\ 6 \end{pmatrix}$, work out

Oct/Nov 2016

Work out the sum $\begin{pmatrix}5\\-1\end{pmatrix} + \begin{pmatrix}-3\\2\end{pmatrix}$.

Oct/Nov 2016

The diagram displays two sides of the rhombus $ABCD$ on a coordinate grid, with points A, B and C marked.

Oct/Nov 2017

Find $\begin{pmatrix} 3 \\ 2 \end{pmatrix} + \begin{pmatrix} -1 \\ 5 \end{pmatrix}$.

Oct/Nov 2017

The diagram shows a coordinate grid with the $x$-axis running horizontally and the $y$-axis running vertically. Point $A$ is marked at $(2,5)$. Point $B$ is marked at about $(-3,-2)$.

Oct/Nov 2017

The vectors are specified as $s = \begin{pmatrix}3\\-1\end{pmatrix}$ and $t = \begin{pmatrix}4\\2\end{pmatrix}$.

Oct/Nov 2017

The grid diagram shows two sides of rhombus $ABCD$ on a coordinate plane. The points visible are marked $A$, $B$ and $C$.

Oct/Nov 2017

Find $6\begin{pmatrix}2\\-1\end{pmatrix}$.

Oct/Nov 2018

Work out the value of $\begin{pmatrix}-2 \\ 5\end{pmatrix} - \begin{pmatrix}-1 \\ 1\end{pmatrix}$.

Oct/Nov 2018

The diagram shows a coordinate grid with the $x$-axis running horizontally and the $y$-axis running vertically. Point $A$ lies in the first quadrant, while point $B$ lies in the second quadrant.

Oct/Nov 2018

Determine $(2,5) - (-3,4)$.

Oct/Nov 2018

Calculate:

Oct/Nov 2019

The diagram displays points $A$, $B$ and $C$ on a coordinate grid.

Oct/Nov 2019

Work out the sum $\begin{pmatrix}2\\-3\end{pmatrix} + \begin{pmatrix}5\\-1\end{pmatrix}$.

Oct/Nov 2020

In the diagram, a rectangle has a line of symmetry at $x = 2$. Two of the rectangle's vertices lie at $(-1,1)$ and $(-1,4)$. The shaded area is given by the inequalities $a \le x \le b$ and $c \le y \le d$.

Oct/Nov 2020

Find $\begin{pmatrix}3\\-2\end{pmatrix} + \begin{pmatrix}-5\\7\end{pmatrix}$.

Oct/Nov 2021

Points $A$ and $B$ are marked on the grid. The $x$-axis is labelled from $-3$ to $3$, and the $y$-axis runs from $-3$ to $4$. Point $B$ appears at the coordinate shown in the diagram, while point $A$ is placed in the lower-left quadrant.

Oct/Nov 2021

Find the answer.

Oct/Nov 2022

Here, $\mathbf{a} = \begin{pmatrix}4\\9\end{pmatrix}$, $\mathbf{b} = \begin{pmatrix}-6\\1\end{pmatrix}$, and $\mathbf{c} = \begin{pmatrix}13\\-2\end{pmatrix}$.

Oct/Nov 2023

The diagram includes a coordinate grid, and point $B$ is marked at $(4, 2)$. The vector $ \vec{AB} = \begin{pmatrix} 3 \\ -2 \end{pmatrix}$.

Oct/Nov 2024

The diagram displays quadrilateral ABCD on a 1 cm^{2} grid.

Oct/Nov 2025

Find B's coordinates.

Oct/Nov 2025