Triangle ABC has vertices A(-2, 3), B(0, 3), and C(-1,-1). Find the coordinates of the image after a reflection over the
x-axis.

Given:

Given that the triangle ABC has vertices A(-2,3), B(0,3) and C(-1,-1).

We need to determine the coordinates of the image after a reflection over the x - axis.

Let A'B'C' denote the coordinates of the triangle after a reflection over the x - axis.

Coordinates of the point A':

The general rule to reflect the coordinate across the x - axis is given by

Substituting the point A(-2,3), we get;

Thus, the coordinates of the point A' is (-2,-3)

Coordinates of the point B':

The general rule to reflect the coordinate across the x - axis is given by

Substituting the point B(0,3), we get;

Thus, the coordinates of the point B' is (0,-3)

Coordinates of the point C':

The general rule to reflect the coordinate across the x - axis is given by

Substituting the point C(-1,-1), we get;

Thus, the coordinates of the point C' is (-1,1)

Hence, the coordinates of the image after a reflection over the x - axis is A'(-2,-3), B(0,-3) and C(-1,1)