Karen Morrison and Nick Hamshaw Solutions for Exercise 3: Exercise 23.3

Write a column vector to describe the translation from $A$ to $B$ and from $A$ to $C$ in each of the following diagram set of diagram.

Copy the diagram onto the squared paper. Translate the triangle $ABC$:

Three units to the right and two units down.

Copy the diagram onto the squared paper. Translate the triangle $ABC$:

Three units to the left and two units down.

Copy the diagram onto the squared paper. Translate the triangle $ABC$:

Three units to the left and two units down.

Copy the diagram onto the squared paper. Translate the triangle $ABC$:

Three units upwards and one unit to the left.

Copy the diagram onto the squared paper. Translate the triangle $\mathrm{ABC}$:

Three units downwards and four units right.

On squared paper, draw $x \text{and} y-$axes and mark the points $A\left(3,5\right),B\left(2,1\right) \text{and} C\left(-1,4\right)$.

Draw triangle $A\text{'}B\text{'}C\text{'}$, the image of triangle $ABC$ under the translation $\left(\begin{array}{c}2\\ -3\end{array}\right)$ and triangle $A"B"C"$ under the translation $\left(\begin{array}{c}4\\ 1\end{array}\right)$.

A rectangle $MNOP$ with vertices $M\left(1,6\right),N\left(5,6\right),O\left(5,3\right) \text{and} P\left(1,3\right)$ is transformed by the translation $\left(\begin{array}{c}-3\\ 2\end{array}\right)$ to produce rectangle $M\text{'}N\text{'}O\text{'}P\text{'}$. Represent this translation accurately on a set of axes.