Enlargement and Combined Transformations

Enlarge the point ($3$, $4$) by scale factor $2$, using $\left(\begin{array}{cc}2& 0\\ 0& 2\end{array}\right)$.

• 1Multiply: top entry = ($2\times 3$) + ($0\times 4$) = $6$. Bottom entry = ($0\times 3$) + ($2\times 4$) = $8$

Answer: ($6$, $8$)

Reflect ($3$, $2$) in the $x$-axis, then rotate the result $90$° anticlockwise. Find the final point.

• 1Reflect first: $\left(\begin{array}{cc}1& 0\\ 0& -1\end{array}\right)$ applied to ($3$, $2$) gives ($3$, $-2$)
• 2Rotate the result: $\left(\begin{array}{cc}0& -1\\ 1& 0\end{array}\right)$ applied to ($3$, $-2$) gives top entry = ($0\times 3$)+($-1\times -2$)=$2$, bottom entry = ($1\times 3$)+($0\times -2$)=$3$

Answer: ($2$, $3$)