Question

what are the coordinates of point $(x,y)$ when it is reflected across the $x$-axis?
$(-x,y)$
$(-y,-x)$
$(x,-y)$
$(y,x)$

Explanation:

Step1: Recall reflection rule

When reflecting a point \((x,y)\) across the \(x -\)axis, the \(x -\)coordinate remains the same, and the \(y -\)coordinate changes its sign.
Let the original point be \(P=(x,y)\). After reflection across the \(x -\)axis, the new point \(P'\) has coordinates \((x,-y)\) because the distance from the \(x -\)axis for the \(y -\)value is preserved but the direction (sign) is reversed.

Answer:

\((x, -y)\) (corresponding to the third option in the given multiple - choice list)