Question

Quadrilaterals
and



are shown on the coordinate grid.







Which sequence of transformations shows that the quadrilaterals are congruent?

A
reflect EFGHEFGHEFGH across the yyy-axis and then translate the image 555 units down

B
rotate EFGHEFGHEFGH 90°90°90° clockwise about the origin and then translate the image 555 units down

C
rotate EFGHEFGHEFGH 90°90°90° clockwise about the origin and then translate the image 555 units to the right

D
reflect EFGHEFGHEFGH across the yyy-axis and then translate the image 555 units to the right

Answer 1

To determine which sequence of transformations shows that the quadrilaterals are congruent, we need to analyze each option:

- **A**: Reflect EFGH across the y-axis and then translate the image 5 units down.
- **B**: Rotate EFGH 90° clockwise about the origin and then translate the image 5 units down.
- **C**: Rotate EFGH 90° clockwise about the origin and then translate the image 5 units to the right.
- **D**: Reflect EFGH across the y-axis and then translate the image 5 units to the right.

For congruence, we must confirm that the resulting coordinates from the transformations precisely match the coordinates of the second quadrilateral.

1. **Reflection across the y-axis** changes the x-coordinates of the points. If a point is at (x, y), it becomes (-x, y).

2. **Rotation 90° clockwise** moves each point according to the rule (x, y) -> (y, -x).

3. **Translation** involves adding/subtracting to the x or y coordinates.

You would need to look at the coordinates of both quadrilaterals before determining which transformation correctly causes congruence.

Without the specific coordinates of the quadrilaterals, I cannot give you the definitive answer. However, generally:

- If quadrilateral EFGH needs to be flipped horizontally (negative x-values) and moved down, then **Option A** is suitable.

- If rotating EFGH makes it align with the second quadrilateral, then **Option B or C** could work.

- If flipping horizontally and moving right works, then **Option D** may be applicable.

Please provide the specific coordinates or drawings of the quadrilaterals so that we can analyze which transformation sequence achieves congruence.