Question

The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and across the x-axis to obtain point C. What are the coordinates of points B and C?

Answer 1

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 $(x,y)$, the reflection of this point across  the x-axis is the point $(x,-y)$. Finally, our point A $(-2, -3)$ changes into:

Point B: $(-2,3)$

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 $(x,y)$, the reflection of this point across  the y-axis is the point $(-x,y)$. Finally, our point A $(-2,-3)$ changes into:

Point C: $(2,-3)$

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Below are illustrated all these points in the coordinate grid.