Question

A figure has a vertex at (-1, -3). If the figure has line symmetry about the x-axis, what are the coordinates of another vertex of the figure?

Answer 1

at other point reflect across x axis
multiply y value by -1

(-1,3) is another vertex

Answer 2

(-1,3).

Explanation:

If the figure has a vertex (-1,-3) , than this point lies in third quadrant. If we revolve the figure about x-axis, the symmetry of the figure will lie in the second quadrant whose x-coordinate is negative and y-coordinate is positive i.e, abscissa is negative and ordinate is positive hence the symmetry of the given figure will lie in a second quadrant.

Hence the coordinates of another vertex of the figure is (-1,3).