Question

Describe a sequence of transformations that shows that personalcongruent to Polygon B'BLAYour answer

Answer 1

We will investigate the sequence of transformations associated with pre-image and image of a polygon.

Two polygons named ( A and B ) are given on a cartesian coordinate grid. Polygon A is congruent to polygon B. The concept of congruency relays that all the inetrior angles and sides of a polygon remains the same.

There is a list of transformations that are allowed:

`\text{Rotation, reflection, translation, dilation}`

However, when we impose the condition that the congruency of polygons we will remove the " dilation " transformation because the stretch or shrink off any figure will violate the condition of transformation. Therefore, the polygons to be remain congruent to one another there are only three possibilities:

`\text{Rotation, reflection, translation}`

We will see what sequence of transformation will impose the polygon A directly onto polygon B. We will investigate each transformation as follows:

`\text{reflection}`

Allows the exact mirror image across any straight line specified. A polygon in the third quadrant can be reflected into the second quadrant by reflection across the line:

`\text{reflection across y = 0 }`

The above gives us an image in the second quadrant.

We see that the new reflection is displaced 3 units to the left of polygon B. So we need to translate the entire reflected image 3 units to the right for it lie on top of polygon B. Therefore,

`\text{Translation to right off 3 units}`

So the sequence of transformations becomes:

`\begin{gathered} \text{reflection across y = 0} \\ \text{Translation to right by 3 units} \end{gathered}`