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R. 18 Checkpoint: Congruence transformations CCR
Which of the following transformations will, when applied to a regular hexagon, produce a congruent hexagon? Select all that apply.
dilation with scale factor 2 centered at the midpoint of one side of the hexagon
dilation with scale factor 3.5 centered at one vertex of the hexagon
reflection across one of the sides of the hexagon
translation 2 units to the right and 9 units down
Submit

R. $18$ Checkpoint: Congruence transformations CCR $\newline$ Which of the following transformations will, when applied to a regular hexagon, produce a congruent hexagon? Select all that apply. $\newline$ dilation with scale factor $2$ centered at the midpoint of one side of the hexagon $\newline$ dilation with scale factor $3$ . $5$ centered at one vertex of the hexagon $\newline$ reflection across one of the sides of the hexagon $\newline$ translation $2$ units to the right and $9$ units down $\newline$ Submit

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Interpret regression lines

Full solution

Q. R.

18

Checkpoint: Congruence transformations CCR

\newline

Which of the following transformations will, when applied to a regular hexagon, produce a congruent hexagon? Select all that apply.

\newline

dilation with scale factor

2

centered at the midpoint of one side of the hexagon

\newline

dilation with scale factor

3

.

5

centered at one vertex of the hexagon

\newline

reflection across one of the sides of the hexagon

\newline

translation

2

units to the right and

9

units down

\newline

Submit

Dilation Not Congruent: A congruent figure is one that is the same size and shape as the original figure. A dilation changes the size of the figure, so a dilation with any scale factor other than $1$ will not produce a congruent figure. Therefore, a dilation with scale factor $2$ centered at the midpoint of one side of the hexagon will not produce a congruent hexagon.
Dilation Not Congruent: Similarly, a dilation with scale factor $3.5$ centered at one vertex of the hexagon will also change the size of the hexagon, making it larger and not congruent to the original hexagon.
Reflection Congruent: A reflection across one of the sides of the hexagon will produce a mirror image of the hexagon on the other side of the line of reflection. Since reflections do not change the size or shape of the figure, the reflected hexagon will be congruent to the original hexagon.
Translation Congruent: A translation moves a figure without rotating or reflecting it. Since a translation does not change the size or shape of the figure, translating the hexagon $2$ units to the right and $9$ units down will produce a hexagon that is congruent to the original hexagon.

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