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GB-35-05-001 · Negative enlargement

Point P is (3,1)(3,1). Enlarge P by scale factor -1 about centre (3,−3)(3,-3). Find its image coordinates.

Transformations: Negative Enlargements Booklet p. 76
Method
1) Find column vector journey from Centre X → P
2) Multiply vector by negative scale factor
3) Add scaled vector to Centre X
Worked Example (GB-35-05-001)
1)
Centre-to-point vector: CP→=(3−(3)1−(−3))=(04)\overrightarrow{CP}=\begin{pmatrix}3-(3)\\1-(-3)\end{pmatrix}=\begin{pmatrix}0\\4\end{pmatrix}.
2)
Multiply that vector by the scale factor: CP′→=−1(04)=(0−4)\overrightarrow{CP'}=-1\begin{pmatrix}0\\4\end{pmatrix}=\begin{pmatrix}0\\-4\end{pmatrix}.
3)
Start at the centre and follow the new vector: P′=(3+(0),−3+(−4))=(3,−7)P'=(3+(0),-3+(-4))=(3,-7).
Ans = (3,−7)(3,-7)