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 the coordinates (1, 2).

When reflecting a point across the x-axis, the x-coordinate remains the same while the y-coordinate changes sign. Therefore, if point A has coordinates (1, -2) before the reflection, its new coordinates after reflection will be (1, 2).

A ((1, 2)) CORRECT

This is the correct answer. If A is at (1, -2), reflecting across the x-axis changes the y-coordinate from -2 to 2, resulting in A' at (1, 2).

B ((1, 4)) YOUR ANSWER

This option suggests that the y-coordinate of point A has changed to 4 after reflection. However, reflecting a point across the x-axis only changes the sign of the y-coordinate; thus, (1, 4) does not accurately reflect the original point's coordinates.

C ((2, 1)) YOUR ANSWER

This choice indicates a change in both x and y coordinates. In a reflection across the x-axis, the x-coordinate remains unchanged while only the y-coordinate's sign is inverted. Thus, (2, 1) cannot be the result of the reflection from any point A.

D ((2, 4)) YOUR ANSWER

This is another incorrect option as it implies both coordinates have changed. Similar to the previous explanations, the x-coordinate should remain constant, and the y-coordinate should only change sign, making (2, 4) an invalid reflection result.

Conclusion

In reflecting points across the x-axis, only the y-coordinate is affected, while the x-coordinate stays the same. The reflection of point A at (1, -2) correctly results in point A' at (1, 2), confirming option A as the only accurate choice. The other options misrepresent the reflection process, as they either change the x-coordinate or incorrectly adjust the y-coordinate.

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 the coordinates (1, 2).

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