GCSE Mathematics (9-1)
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    1. Point P=(2,−1)P=(2,-1) is translated by (−43)\begin{pmatrix}-4\\3\end{pmatrix}. Give the image coordinates.
    2. Find the vector from A=(−3,2)A=(-3,2) to B=(1,−4)B=(1,-4). Give a column vector.
    3. Describe the translation represented by (5−2)\begin{pmatrix}5\\-2\end{pmatrix}.
    4. An arrow starts at (4,−2)(4,-2) and represents (−35)\begin{pmatrix}-3\\5\end{pmatrix}. Give its endpoint.
    5. Write the vector from (2,5)(2,5) to (−3,1)(-3,1) as a column.
    6. A point moves 6 units left and 3 units up. Write its translation as a column vector.
    7. An arrow starts at (1,1)(1,1) and ends at (4,3)(4,3). Write its column vector.
    8. A point moves by (3−2)\begin{pmatrix}3\\-2\end{pmatrix} and then by (−74)\begin{pmatrix}-7\\4\end{pmatrix}. Give the total horizontal and vertical changes.
    Answers and concise solutions

    1. Image of P

    Answer: (−2,2)(-2,2): add the vector components to the coordinates.

    2. Vector AB

    Answer: AB→=(4−6)\overrightarrow{AB}=\begin{pmatrix}4\\-6\end{pmatrix}.

    3. Translation

    Answer: 5 units right and 2 units down.

    4. Endpoint

    Answer: (1,3)(1,3).

    5. Column vector

    Answer: (−5−4)\begin{pmatrix}-5\\-4\end{pmatrix}: 5 left and 4 down.

    6. Translation vector

    Answer: (−63)\begin{pmatrix}-6\\3\end{pmatrix}.

    7. Vector

    Answer: (32)\begin{pmatrix}3\\2\end{pmatrix}.

    8. Total change

    Answer: Horizontal change −4-4 and vertical change 22, so the total vector is (−42)\begin{pmatrix}-4\\2\end{pmatrix}.

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