Vectors and translation vectorsIB MYP Maths Extended: Flashcards

What these 13 flashcards ask

How do you find \overrightarrow{AB} from the coordinates of A and B?
\overrightarrow{BA} in terms of \overrightarrow{AB}?
\begin{pmatrix}a\\ b\end{pmatrix}+\begin{pmatrix}c\\ d\end{pmatrix}?
k\begin{pmatrix}a\\ b\end{pmatrix}?
Magnitude of \begin{pmatrix}x\\ y\end{pmatrix}?
Magnitude of \begin{pmatrix}5\\ -12\end{pmatrix}?
What does the translation \begin{pmatrix}3\\ -2\end{pmatrix} do?
Image of (2,5) under \begin{pmatrix}3\\ -2\end{pmatrix}?
How do you reverse a translation \mathbf v?
Single translation for \begin{pmatrix}4\\ 3\end{pmatrix} then \begin{pmatrix}-7\\ 2\end{pmatrix}?
When are two vectors parallel?
In parallelogram ABCD, which vectors are equal?
Position vector of the midpoint M of [AB]?

Exam questions on Vectors and translation vectors

The vectors $\mathbf p$ and $\mathbf q$ are given by $\mathbf p=\begin{pmatrix}3\\ -2\end{pmatrix}$ and $\mathbf q=\begin{pmatrix}-1\\ 4\end{pmatrix}$ .
The point $A(2,5)$ is translated by $\mathbf p$ and then by $\mathbf q$ . Find the coordinates of its final image.2 marks
$ABCD$ is a parallelogram, with the vertices in that order, and $A(1,1)$ , $B(6,2)$ and $C(9,6)$ .
Find the exact length of the diagonal $[AC]$ .2 marks
A drone starts at the point $S(2,-1)$ on a map grid, where one unit on the grid is 1 km. It makes a translation $\begin{pmatrix}4\\ 3\end{pmatrix}$ and then a translation $\begin{pmatrix}-7\\ 2\end{pmatrix}$ to reach the point $T$ .
Find the coordinates of $T$ , and write down the single translation that takes $S$ directly to $T$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).