11.1 Use the rectangular coordinate system  (Page 2/13)

Solution

The coordinate values are the same for both points, but the $x$ and $y$ values are reversed. Let’s begin with point $(1,3).$ The $x\text{-coordinate}$ is $1$ so find $1$ on the $x\text{-axis}$ and sketch a vertical line through $x=1.$ The $y\text{-coordinate}$ is $3$ so we find $3$ on the $y\text{-axis}$ and sketch a horizontal line through $y=3.$ Where the two lines meet, we plot the point $(1,3).$

To plot the point $(3,1),$ we start by locating $3$ on the $x\text{-axis}$ and sketch a vertical line through $x=3.$ Then we find $1$ on the $y\text{-axis}$ and sketch a horizontal line through $y=1.$ Where the two lines meet, we plot the point $(3,1).$

Notice that the order of the coordinates does matter, so, $\left(1,3\right)$ is not the same point as $\left(3,1\right).$

Solution

The first number of the coordinate pair is the $x\text{-coordinate},$ and the second number is the $y\text{-coordinate}.$

ⓐ Since $x=\mathrm{-1},y=3,$ the point $\left(\mathrm{-1},3\right)$ is in Quadrant II.

ⓑ Since $x=\mathrm{-3},y=\mathrm{-4},$ the point $\left(\mathrm{-3},\mathrm{-4}\right)$ is in Quadrant III.

ⓒ Since $x=2,y=\mathrm{-1},$ the point $(2,\mathrm{-1})$ is in Quadrant lV.

ⓓ Since $x=3,y=\frac{5}{2},$ the point $\left(3,\frac{5}{2}\right)$ is in Quadrant I. It may be helpful to write $\frac{5}{2}$ as the mixed number, $2\frac{1}{2},$ or decimal, $2.5.$ Then we know that the point is halfway between $2$ and $3$ on the $y\text{-axis}.$

Solution

As we locate the $x\text{-coordinate}$ and the $y\text{-coordinate},$ we must be careful with the signs.