DP Mathematics: Applications and Interpretation Questionbank

Describe, in words, the effect of the transformation $T$.

Show that the points $\text{A}(1, 4), \text{B}(4, 8), \text{C}(8, 5), \text{D}(5, 1)$ form a square.

Determine the area of this square.

Find the coordinates of $\text{A', B', C', D'}$, the points to which $\text{A, B, C, D}$ are transformed under $T$.

Show that $\text{A' B' C' D'}$ is a parallelogram.

Determine the area of this parallelogram.

Write down ${\mathit{A}}_n$, in terms of $n$.

Write down ${\mathit{A}}_1$.

Find the coordinates of the image of the point $(6, -2)$.

A triangle $L$ with vertices lying on the $xy$ plane is transformed by $T$.

Explain why both $L$ and its image will have exactly the same area.

Given that $T:\left(\begin{array}{c}p\\ q\end{array}\right)\mapsto 2\left(\begin{array}{c}p\\ q\end{array}\right)$, find the value of $p$ and the value of $q$.

Find a single matrix $\mathit{P}$ that defines a transformation that represents the overall change in position.

Write down each of the transformations in matrix form, clearly stating which matrix represents each transformation.

Three drones are initially positioned at the points $\text{A}$, $\text{B}$ and $\text{C}$. After performing the movements listed above, the drones are positioned at points $\text{A}\prime$, $\text{B}\prime$ and $\text{C}\prime$ respectively.

Show that the area of triangle $\text{ABC}$ is equal to the area of triangle $\text{A}\prime \text{B}\prime \text{C}\prime$ .

Find a single transformation that is equivalent to the three transformations represented by matrix $\mathit{P}$.

Find ${\mathit{P}}^2$.

Hence state what the value of ${\mathit{P}}^2$ indicates for the possible movement of the drone.

Show that the equation of the resulting line does not depend on $m$ or $c$.

Find an expression for$h\left(x\right)$.

Find the value of $a$.

Find the value of $b$.

By considering the image of $(0, 0)$, find $\mathit{q}$.

By considering the image of $(1, 0)$ and $(0, 1)$, show that

$\mathit{P}=\left(\begin{array}{cc}\frac{\sqrt{3}}{4} & \frac{1}{4}\\ -\frac{1}{4} & \frac{\sqrt{3}}{4}\end{array}\right)$.

Write down the matrix $\mathit{S}$.

Use $\mathit{P}=\mathit{R}\mathit{S}$ to find the matrix $\mathit{R}$.

Write down an equation satisfied by $\left(\begin{array}{c}a\\ b\end{array}\right)$.

Hence find the angle and direction of the rotation represented by $\mathit{R}$.

Find the value of $a$ and the value of $b$.

Find the area of the image of P.

Find the area of triangle X.

Describe fully the geometrical transformation represented by X.

Describe fully the geometrical transformation represented by B.

Hence find the area of triangle Y.

Find the matrix X.

Describe fully the geometrical transformation represented by A.

Find the coordinates of triangle X.

Matrix A represents a combination of transformations:            

A stretch, with scale factor 3 and y-axis invariant;
Followed by a stretch, with scale factor 4 and x-axis invariant;
Followed by a transformation represented by matrix C.

Find matrix C.