A triangle with vertices Au *b(0iu ir.io(6,6), B(3,1) and C(1,3) is transformed by x′=Ax+b
where A = $\begin{pmatrix}
-1&2 \\
-2&1
\end{pmatrix}$and b = $\begin{pmatrix}
-6 \\
3
\end{pmatrix}$.
1.On the following grid, draw the image of the triangle ABC.




2.Given the area of the triangle ABC is 16 $units^2$, find the area of its image.    $units^2$

  A triangle with vertirc 6g/s4 - p9cpkqxyqb 8)glw5ces $\mathrm{A}(2,5), \mathrm{B}(6,-5) $ and $\mathrm{C}(-4,-5)$ is transformed by $\mathbf{x}^{\prime}=\mathbf{A} \mathbf{x}+\mathbf{b}$ where $\mathbf{A}=\left(\begin{array}{cc}1 & -0.2 \\ 0.5 & -0.4\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}-1 \\ -2\end{array}\right)$ .
1. On the following grid, draw the image of the triangle A B C .

2.Find the area, in square units, of the image of the triangle ABC.    $units^2$

  The geometric transformatikggp3m -* 8tmvon $ \left(\begin{array}{l}x^{\prime} \\ y^{\prime}\end{array}\right)=\left(\begin{array}{ll}2 & -3 \\ 5 & -2\end{array}\right)\left(\begin{array}{l}x \\ y\end{array}\right)+\left(\begin{array}{c}-4 \\ 1\end{array}\right) $maps points with coordinates (x, y) to points with coordinates $\left(x^{\prime}, y^{\prime}\right) $.
1. Find the coordinates of the image of the point:
(1) A(1,-6) ;(a,b) a=   b=  
(2) B(3 b, b) where $b \in \mathbb{R}$ .(a,b) a=   b=  
2. Determine the coordinates of point P whose image is $P^{\prime}(11,22)$ ;(a,b) a=   b=  

A linear transformation maps the point A(2,3) to A ′(2,−5) and them86gy 60 gxfrd point B(−2,1) to B ′(6,9). Determine the ling6dmf 0 xr68gyear transformation, giving your answer in the form x′=Ax where A is a 2×2 matrix.

  A circle defined by tko5c afms;5 71s0niulf2 n3dvhe equation $x^{2}+y^{2}=\frac{20}{4}$ is horizontally stretched by a scale factor of $\frac{8}{5}$ and then translated by the vector $\left(\begin{array}{l}0 \\ \frac{5}{2}\end{array}\right)$ .
1. On the following grid, draw the image of the circle.

2.Find the area of the image of the circle, giving your answer in terms of π.    π

  A circle defined by the eqw+l2cbc : w jrp1vcz,)uation $x^{2}+y^{2}=\frac{y}{4}$ is vertically stretched by a scale factor of $\frac{10}{3}$ and then translated by the vector $\left(\begin{array}{c}-3 \\ 0\end{array}\right)$ .
1. On the following grid, draw the image of the circle.

2.Find the area of the image of the circle, giving your answer in terms of $π$. $\frac{aπ}{b}$ a =    b =   

  A triangle with vertices A(3,5), B(5,2) and C(3,2) is rotated1iy/j1. q uj,h,q u.itwl7wwin 1l3 eq $90^{\circ}$ anticlockwise about O(0,0) and then reflected in the line y=−x. The rotation is represented by matrix A and reflection by matrix B.
1.Write down the matrix :
(1)A; $\begin{pmatrix}
a&b \\
c&d
\end{pmatrix}$ a =    b =    c =    d =   
(2)B.$\begin{pmatrix}
a&b \\
c&d
\end{pmatrix}$ a =    b =    c =    d =   
2.Find the matrix that represents the rotation followed by the reflection. BA = $\begin{pmatrix}
a&b \\
c&d
\end{pmatrix}$ a =    b =    c =    d =   
3.On the following grid, draw the image of the triangle ABC.

  Parallelogram ABCD is transltzwj93q n;cw9 y;iq 0x*mime3ated by the vector $\left(\begin{array}{l}1 \\ 4\end{array}\right)$ , then enlarged by a scale factor of $\frac{3}{2} $ from the origin and then reflected in the y -axis.
1. Determine a single transformation that maps the parallelogram A B C D to its image. Give your answer in the form
$\mathbf{x}^{\prime}=\mathbf{A} \mathbf{x}+\mathbf{b} \text {. }$
The area of the image is equal to k times the area of parallelogram A B C D .
2. Find the value of k .$\frac{a}{b}$a =    b =   

  A triangle with vertices *rkc/dvaf;l *$\mathrm{A}(-3,3), \mathrm{B}(3,2) $ and $\mathrm{C}(-1,1)$ is rotated $90^{\circ} $ clockwise about $ \mathrm{O}(0,0) $ and then enlarged by a scale factor of 2 .
The matrix $ \mathbf{E}=\left(\begin{array}{ll}2 & 0 \\ 0 & 2\end{array}\right)$ represents the enlargement with a scale factor of 2.
1. On the following grid, draw the image of the triangle A B C .

2.Given the area of the triangle ABC is 5 $units^2$, find the area of its image.    $units^2$

  Trapezoid PQRS is try- ho+47fgrx.r.sj v* v vw+n m.4asvg6dmn 5vanslated by the vector $\left(\begin{array}{c}-7 \\ 2\end{array}\right)$ , then vertically stretched by a scale factor of $\frac{5}{3}$ and then reflected in the x -axis.
1. Determine a single transformation that maps the trapezoid PQRS to its image. Give your answer in the form $\mathbf{x}^{\prime}=\mathbf{A x}+\mathbf{b}$ The area of the image is equal to k times the area of the trapezoid PQRS.
2. Find the value of k . $\frac{a}{b}$ a =    b =   

  Consider the geometric transfo3 b8os7sl;q /ep af xqz9q4h k(k0tgp3rmation
$\left(\begin{array}{l}
x^{\prime} \\
y^{\prime}
\end{array}\right)=\left(\begin{array}{cc}
3 & a \\
3 & b-3
\end{array}\right)\left(\begin{array}{l}
x \\
y
\end{array}\right)+\left(\begin{array}{c}
b \\
a-9
\end{array}\right) .$
that maps points from (x, y) to $\left(x^{\prime}, y^{\prime}\right)$ .
It is given that the transformation maps the point (4,-4) to the point (-4,-11) .
1. Show that a=6 and b=8 .
2. Given that the transformation maps the point (p, q) to itself, find the value of p and the value of q .
A rectangle R with vertices lying on the x y -plane undergoes this transformation. p =    q =   
3. Show that the area of the image is three times the size of R .

  A geometric transformation T :b8a zhf rnguu-)c0g4. $\left(\begin{array}{l}x \\ y\end{array}\right) \mapsto\left(\begin{array}{c}x \\ y^{\prime}\end{array}\right)$ is defined by
$\left(\begin{array}{l}
x^{\prime} \\
y^{\prime}
\end{array}\right)=\left(\begin{array}{cc}
\cos \left(\frac{\pi}{3}\right) & \sin \left(\frac{\pi}{3}\right) \\
\sin \left(\frac{\pi}{3}\right) & \cos \left(\frac{\pi}{3}\right)
\end{array}\right)\left(\begin{array}{l}
x \\
y
\end{array}\right)-\frac{\sqrt{3}}{2}\left(\begin{array}{l}
1 \\
2
\end{array}\right)$ .
1. Find the coordinates of the image of the point $P(1,-\sqrt{3})$ . $\left(-a-\frac{\sqrt{b}}{c},-\sqrt{d}\right) $ a =    b =    c =    d =   
2. Given that T : $\left(\begin{array}{l}a \\ b\end{array}\right) \mapsto \frac{1}{2}\left(\begin{array}{l}a \\ b\end{array}\right)$ , find the value of a and the value of b . a =    b =   
A rhombus R with vertices lying on the x y -plane is transformed by T .
3. Show that the area of the image is half the size of R .