In the xy-plane, parallelogram ABCD is to be reflected across the x-axis to form parallelogram A'B'C'D'. What will the coordinates of A' be?

Rationale

A' will have coordinates (1, 2).

Reflecting a point across the x-axis changes the sign of its y-coordinate while keeping the x-coordinate the same. Therefore, if point A has coordinates (1, -2), its reflection A' will have coordinates (1, 2).

A ((1, 2)) CORRECT

This option is the correct reflection of point A across the x-axis. If the original coordinates of point A are (1, -2), the reflection will become (1, 2), confirming that this choice accurately represents the result of the transformation.

B ((1, 4)) YOUR ANSWER

This choice suggests that the y-coordinate of point A has changed to 4 after reflection, which is incorrect. The reflection across the x-axis only alters the sign of the y-coordinate, meaning it cannot produce a y-coordinate of 4 if the original was negative.

C ((2, 1)) YOUR ANSWER

This option incorrectly changes both the x and y coordinates of point A. The reflection across the x-axis maintains the x-coordinate, which means it cannot result in a new x-coordinate of 2 if the original was 1.

D ((2, 4)) YOUR ANSWER

This choice also alters both coordinates incorrectly. The x-coordinate should remain 1, and the y-coordinate should reflect the original y-coordinate's sign. Therefore, this option does not represent the correct outcome of the reflection.

Conclusion

When reflecting a point across the x-axis, only the sign of the y-coordinate is affected, while the x-coordinate remains unchanged. Given the transformation from point A to A', the coordinates (1, 2) correctly represent the new position after reflection. Other options fail to adhere to the rules of reflection, leading to incorrect coordinate transformations.

In the xy-plane, parallelogram ABCD is to be reflected across the x-axis to form parallelogram A'B'C'D'. What will the coordinates of A' be?

A' will have coordinates (1, 2).

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