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GB-35-04-001 · Enlargement with a centre

Point P is (4,−5)(4,-5). Enlarge P by scale factor 3 about centre (−6,5)(-6,5). Find its image coordinates.

Transformations: Enlargements from a Centre Booklet p. 76
Method
1) Find column vector journey from Centre X → P
2) Multiply vector by scale factor
3) Add scaled vector to Centre X
Worked Example (GB-35-04-001)
1)
Centre-to-point vector: CP→=(4−(−6)−5−(5))=(10−10)\overrightarrow{CP}=\begin{pmatrix}4-(-6)\\-5-(5)\end{pmatrix}=\begin{pmatrix}10\\-10\end{pmatrix}.
2)
Multiply that vector by the scale factor: CP′→=3(10−10)=(30−30)\overrightarrow{CP'}=3\begin{pmatrix}10\\-10\end{pmatrix}=\begin{pmatrix}30\\-30\end{pmatrix}.
3)
Start at the centre and follow the new vector: P′=(−6+(30),5+(−30))=(24,−25)P'=(-6+(30),5+(-30))=(24,-25).
Ans = (24,−25)(24,-25)