Question Type 4: Visually applying simple matrix transformations Exercises

A rectangle has vertices $(1, 1), (4, 1), (4, 3), (1, 3)$. Reflect it in the line $x=2$, then apply a vertical stretch by factor 2. Find the final coordinates.

Determine the single $2 \times 2$ matrix representing first an enlargement by factor 2 about the origin, then a reflection in the line $y=0$.

Find the $2\times2$ matrix representing first a horizontal stretch by factor 3, then a vertical stretch by factor 2 in the plane.

The mapping $T:(x,y)\mapsto(3x+1, 3y-2)$. (a) Describe $T$ as an enlargement followed by a translation. (b) Describe $T$ as a horizontal stretch, a vertical stretch, and translations.

Let $f(x)=x^2$. Perform a horizontal stretch by factor $\frac{1}{2}$, then a vertical stretch by factor 4. Write down the equation of the transformed function $g(x)$.

A function $f(x)$ is first subjected to a vertical stretch by factor 5 about the $x$-axis, then a horizontal stretch by factor 2 about the $y$-axis. Write the equation of the resulting function in terms of $f$.

Given point $A(2,1)$, apply an enlargement of scale factor $3$ centred at the origin, then translate by vector $\begin{pmatrix} 0 \\ 3 \end{pmatrix}$. Find the coordinates of the image $A'$.

Triangle $ABC$ has vertices $A(1,2)$, $B(3,1)$ and $C(2,4)$. Reflect it in the $y$-axis, then enlarge by a scale factor of 2 about the origin. Find the coordinates of $A'$, $B'$, $C'$.

The function $f(x)=\frac{1}{x}$ is mapped to $h(x)=-\frac{1}{x}+2$. Describe the sequence of transformations that takes $f$ to $h$.

The graph of $y=f(x)$ is transformed to $y=g(x)=-2f(3x)+5$. Describe each transformation in order.