Explain why when you reflect a point across the line , the −coordinate and the −coordinate change places, and when you reflect a point across the line , the −coordinate and the −coordinate change places and their signs are changed.

This is a reflection; a reflection can be seen as folding an object over the line of reflection. Normally, the original object is referred to as pre-image, while the reflection is called image.

Explanation:

Mathematically when a point reflect across the X, axis, the X coordinate remains same, however, when the Y, coordinate is transformed into opposite, the sign changes.

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.

answer; fulfilling a goal of the president's council of physical fitness and sports;