Exercise 1 Page 107

We want to describe the relationship between these two points with rational coordinates. Looking at the coordinates, we can see that the $y\text{-}$coordinates of the points are opposite numbers. We know this because they are the same value with opposite signs. Also, the $x\text{-}$coordinates of the points are the same. Let's now take a look at the location of the points. We are going to plot each point on a coordinate plane. Here are the steps to follow when we plot a coordinate pair $(x,y)$ on a coordinate plane.

1. First, we find $x$ on the $x\text{-}$axis.
2. We move up or down $y$ units from $x$ on the $x\text{-}$axis. The direction depends on the sign of $y.$
3. We draw a point at the location.

The coordinates of our point are $\left(9,\text{-}\frac{2}{5}\right).$ Following Step $1,$ let's find $x=9$ on the $x\text{-}$axis. Here it is.

Now, notice that the $y\text{-}$coordinate of the point is negative. When the $y\text{-}$coordinate is negative, we move down. When the $y\text{-}$coordinate is positive, we move up. This means we should move down $\frac{2}{5}$ units.

The arrow points at the location of our point. Let's place a point there.

We can follow the same steps to plot point $(9,\frac{2}{5}).$ Here are the results.

Notice that one point is a reflection of the other point across the $x\text{-}$axis.