To analyze the transformation of the parallelogram HIJK into H'I'J'K', we will consider each step of the transformation:
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Translation 3 units to the right: This transformation affects the x-coordinates of the vertices of parallelogram HIJK. If the original vertices are represented as points \((x, y)\), after translating them 3 units to the right, the new coordinates will be \((x + 3, y)\).
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Reflection across the x-axis: This transformation affects the y-coordinates of the points. Reflecting a point across the x-axis changes the sign of the y-coordinate. So, if after the translation, a point is \((x + 3, y)\), reflecting it gives us \((x + 3, -y)\).
Now, we can conclude several statements about the new parallelogram H'I'J'K':
- The shape and size of the parallelogram remain unchanged after these transformations.
- The new parallelogram H'I'J'K' will have corresponding sides that are parallel to the sides of HIJK, consistent with the properties of parallelograms.
- The new position of the parallelogram will be shifted 3 units to the right and mirrored over the x-axis.
In summary, a true statement regarding the transformation of the parallelogram HIJK to H'I'J'K' could be:
"The new parallelogram H'I'J'K' is the same size and shape as HIJK but is translated 3 units to the right and reflected over the x-axis."
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