What will be the coordinates of B''?
The coordinates of B'' are (-1,-4).
To determine the coordinates of B'', we analyze the transformation applied to the original point B. In this case, B has been reflected across the x-axis and translated downwards, resulting in the coordinates (-1, -4).
This point reflects a negative x-coordinate and a positive y-coordinate, which does not align with the transformation described. A reflection across the x-axis would not yield a positive y-coordinate, as it would change the sign of the y-coordinate from positive to negative.
While the x-coordinate is negative, the y-coordinate is still not correct. The transformation requires a specific downward movement that affects the y-coordinate more significantly, leading to a value of -4 instead of -1. Thus, this choice does not represent the final coordinates after the transformation.
This option has a positive x-coordinate, which is incorrect based on the reflection over the x-axis. The original point's x-coordinate must remain negative after the transformation, hence the x-coordinate of 1 is not valid. The y-coordinate of -4 is correct, but the x-coordinate disqualifies this choice.
This choice correctly reflects the x-coordinate as negative and the y-coordinate as -4. It accurately represents the transformation applied to point B, confirming that it is the final coordinates of B'' after the reflection and downward translation.
The coordinates of B'' are determined through the transformation process, which involved reflecting B across the x-axis and translating it downwards. Among the provided options, (-1, -4) accurately reflects the resultant coordinates, while the other choices fail to meet the criteria established by the transformation. Understanding these transformations is crucial in geometry, especially when analyzing points in a Cartesian coordinate system.
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