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# The vertices of a triangle ABC are given by the coordinates A(3, 2), B(0, 4) and C(5, 3). Triangle ABC is mapped onto triangle A'B'C', the coordinates of its vertices being $\mathrm{A}^{\prime}\left(-3, \frac{9}{2}\right) \mathrm{B}^{\prime}(-6,0)$ and $\mathrm{C}^{\prime}\left(-\frac{9}{2}, \frac{15}{2}\right)$. a) Find the matrix which maps ABC onto A'B'C'. b) Find the matrix which maps A'B'C' onto ABC.

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$A(3,2),B(0,4),C(5,3)$

$A'\left(-3,\dfrac{9}{2}\right), B'(-6,0), C'\left(-\dfrac{9}{2},\dfrac{15}{2}\right)$

We are given the triangles $ABC$ and $A'B'C'$:

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