Vectors and translation vectorsIB MYP Maths Extended: Mind map

Exam questions on Vectors and translation vectors

1. 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
2. $ABCD$ 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
3. 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