<u>Given</u>:
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.
<u>Coordinates of the point A':</u>
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)
<u>Coordinates of the point B':</u>
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)
<u>Coordinates of the point C':</u>
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)