Question

1. Find a sequence of rigid motions and

dilations that takes square ABCD to

square EFGH.

Answer 1

Answer:

Rotation counterclockwise (45º) and Dilation by a scale factor of 5/2.

Step-by-step explanation:

1) Completing the question: check the figure below

2) Rotation counterclockwise (45º). This angle of rotation does not have a simple rule of transformation as with 90º, 180º, 270º, 360º. This new coordinates can be found using a Rotation Matrix.

To find each point after rotation:

$A=\begin{bmatrix}x\\ y\end{bmatrix},A'=\begin{bmatrix}x\\ y\end{bmatrix}*\begin{pmatrix}cos45^{\circ} & -sin45^{\circ}\\ sin45^{\circ}& cos45^{\circ}\end{pmatrix}$

Similarly do the same for B, C, and D to find B', C' and D'.

3) Dilation by a scale factor of 5/2

Pre image

Dilated one:

$D\frac{5}{2}(x,y)$

Answer 2

Rigid motions are transformations that preserve side lengths and angle measure.

• The rigid motion is rotation of ABCD
• The dilation of ABCD by a scale factor of 2/5

From the question (see attachment), we can see that both shapes are squares, and ABCD has to be rotated, as the first step in getting square EFGH

This means that, the rigid motion is rotation.

Also, the side lengths of both squares are not the same.

So, ABCD has to be dilated to get EFGH, after being rotated.

The scale of dilation (k) is then calculated as:

$k= \frac{EFGH}{ABCD}$

So, we have:

$k= \frac{2}{5}$

Hence, the dilation of ABCD is by a scale factor of 2/5

Read more about transformation at:

https://brainly.com/question/4289712