Answer:
When reflecting a point or line segment across the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. In this case, we are given the points A (2,5) and B (-3,6) and asked to find their reflections in the x-axis, represented by the points A’ and B’.To reflect point A across the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same. So, if A is (2,5), its reflection A’ is (2,-5). We can follow the same procedure for point B. If B is (-3,6), its reflection B’ is (-3,-6).From this calculation, we see that answer choice A is the correct one. Therefore, A’(2,-5) and B’(-3,6) represent the points that are the reflections of A and B, respectively, across the x-axis.The reflection of a point across the x-axis can also be visualized as the point being mirrored across the x-axis as if it were a horizontal mirror. In this case, point A is reflected to the point A’ which is the same distance above the x-axis as A is below the x-axis. Similarly, point B is reflected to point B’ which is the same distance below the x-axis as B is above the x-axis.It’s also worth noting that reflecting a point or line segment across the x-axis is an example of a transformation in coordinate geometry. Translations, reflections, rotations, and dilations are all examples of transformations that can be used to manipulate geometric figures on the coordinate plane.Overall, reflecting a point or line segment across the x-axis is a relatively simple calculation that involves negating the y-coordinate. In the context of coordinate geometry, it’s important to understand the basic transformations like these and how they can be used to manipulate shapes and figures on the coordinate plane.
Explanation: