A reflection is a common type of transformation. To reflect a point across the x-axis, we consider this axis to be a mirror. On the other hand, if you want to reflect a point across the y-axis, you need to consider this axis to be a mirror. A coordinate grid is the rectangular coordinate system. Just as we can represent real numbers by points on a real number line, we can represent ordered pairs of real numbers by points in a plane called the rectangular coordinate system, or the Cartesian plane. So:
1. Point B.
If you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate changes into its opposite. So, if we have a point [tex](x,y)[/tex], the reflection of this point across the x-axis is the point [tex](x,-y)[/tex]. Finally, our point A [tex](-2, -3)[/tex] changes into:
Point B: [tex](-2,3)[/tex]
2. Point C.
If you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate changes into its opposite. So, if we have a point [tex](x,y)[/tex], the reflection of this point across the y-axis is the point [tex](-x,y)[/tex]. Finally, our point A [tex](-2,-3)[/tex] changes into:
Point C: [tex](2,-3)[/tex]
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Below are illustrated all these points in the coordinate grid.
