Respuesta :
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:
[tex]\text{Rotation, reflection, translation, dilation}[/tex]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:
[tex]\text{Rotation, reflection, translation}[/tex]We will see what sequence of transformation will impose the polygon A directly onto polygon B. We will investigate each transformation as follows:
[tex]\text{reflection}[/tex]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:
[tex]\text{reflection across y = 0 }[/tex]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,
[tex]\text{Translation to right off 3 units}[/tex]So the sequence of transformations becomes:
[tex]\begin{gathered} \text{reflection across y = 0} \\ \text{Translation to right by 3 units} \end{gathered}[/tex]