To determine which sequence of transformations demonstrates that the quadrilaterals \(EFGH\) and \(E'F'G'H'\) are congruent, we need to analyze each option regarding how the quadrilateral will change its position.
-
Option A: Rotate \(EFGH\) 90° clockwise about the origin and then translate the image 5 units to the right.
- Rotation changes the orientation and position.
- Translation moves it without changing its shape/size. This could potentially match the second quadrilateral, depending on its position.
-
Option B: Reflect \(EFGH\) across the y-axis and then translate the image 5 units to the right.
- Reflection will flip the quadrilateral over the y-axis, changing its orientation but keeping it congruent.
- Translating after that could help in matching the second quadrilateral's position.
-
Option C: Rotate \(EFGH\) 90° clockwise about the origin and then translate the image 5 units down.
- Similar to Option A, this will change its orientation and position, and could match the resulting quadrilateral after translation.
-
Option D: Reflect \(EFGH\) across the y-axis and then translate the image 5 units down.
- This reflection will change the orientation across the y-axis, and moving it down will help match the second quadrilateral.
To find the correct option, one needs to visually or analytically confirm the initial positions and orientations of both quadrilaterals \(EFGH\) and \(E'F'G'H'\). The option that properly transforms \(EFGH\) into the new orientation and position as represented by \(E'F'G'H'\) will indicate congruence.
Without a visual representation of the quadrilaterals, we cannot definitively state which option is correct. However, any option that successfully matches the orientation and position will demonstrate congruence.
If you have access to the visual of the quadrilaterals, check which transformation or combination successfully places \(EFGH\) into the location and orientation of \(E'F'G'H'\).
1 answer