11.1 Use the rectangular coordinate system  (Page 3/13)

Solution

1. ⓐ Since $x=0,$ the point whose coordinates are $\left(0,5\right)$ is on the $y\text{-axis}.$
2. ⓑ Since $y=0,$ the point whose coordinates are $\left(4,0\right)$ is on the $x\text{-axis}.$
3. ⓒ Since $y=0,$ the point whose coordinates are $\left(\mathrm{-3},0\right)$ is on the $x\text{-axis}.$
4. ⓓ Since $x=0$ and $y=0,$ the point whose coordinates are $\left(0,0\right)$ is the origin.
5. ⓔ Since $x=0,$ the point whose coordinates are $\left(0,\mathrm{-1}\right)$ is on the $y\text{-axis}.$

Solution

Point A is above $\mathrm{-3}$ on the $x\text{-axis},$ so the $x\text{-coordinate}$ of the point is $\mathrm{-3}.$ The point is to the left of $3$ on the $y\text{-axis},$ so the $y\text{-coordinate}$ of the point is $3.$ The coordinates of the point are $\left(\mathrm{-3},3\right).$

Point B is below $\mathrm{-1}$ on the $x\text{-axis},$ so the $x\text{-coordinate}$ of the point is $\mathrm{-1}.$ The point is to the left of $\mathrm{-3}$ on the $y\text{-axis},$ so the $y\text{-coordinate}$ of the point is $\mathrm{-3}.$ The coordinates of the point are $\left(\mathrm{-1},\mathrm{-3}\right).$

Point C is above $2$ on the $x\text{-axis},$ so the $x\text{-coordinate}$ of the point is $2.$ The point is to the right of $4$ on the $y\text{-axis},$ so the $y\text{-coordinate}$ of the point is $4.$ The coordinates of the point are $\left(2,4\right).$

Point D is below $4$ on the $x-\text{axis},$ so the $x\text{-coordinate}$ of the point is $4.$ The point is to the right of $\mathrm{-4}$ on the $y\text{-axis},$ so the $y\text{-coordinate}$ of the point is $\mathrm{-4}.$ The coordinates of the point are $\left(4,\mathrm{-4}\right).$

Solution

1. Point A is on the x -axis at $x=-4.$ The coordinates of point A are $(-4,0).$
2. Point B is on the y -axis at $y=-2.$ The coordinates of point B are $(0,-2).$
3. Point C is on the x -axis at $x=3.$ The coordinates of point C are $(3,0).$
4. Point D is on the y- axis at $y=1.$ The coordinates of point D are $(0,1).$