좌표평면과 함수

$2$

$16$

$5$

• ⓐ Read the number below the Residence Halls, $4,$ and the letter to the side, A. So the Residence Halls are in grid section 4A.
• ⓑ Find $4$ across the bottom of the map and C along the side. Look below the $4$ and next to the C. Tiger Field is in grid section 4C.

• ⓐ 1C
• ⓑ Engineering Building

• ⓐ 1A
• ⓑ Library

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, $(1,3)$ is not the same point as $(3,1).$

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

ⓐ Since $x=-1,y=3,$ the point $(-1,3)$ is in Quadrant II.

ⓑ Since $x=-3,y=-4,$ the point $(-3,-4)$ is in Quadrant III.

ⓒ Since $x=2,y=-1,$ the point $(2,-1)$ 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 $y\text{-axis}.$

(a) Quadrant II, (b) Quadrant III, (c) Quadrant IV, (d) Quadrant II

(a) Quadrant II, (b) Quadrant II, (c) Quadrant IV, (d) Quadrant II

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

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

Point A is above $-3$ on the $x\text{-axis},$ so the $x\text{-coordinate}$ of the point is $-3.$ 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 $(-3,3).$

Point B is below $-1$ on the $x\text{-axis},$ so the $x\text{-coordinate}$ of the point is $-1.$ 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 $(-1,-3).$

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 $(2,4).$

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 $-4$ on the $y\text{-axis},$ so the $y\text{-coordinate}$ of the point is $-4.$ The coordinates of the point are $(4,-4).$

1. A: (5,1)
2. B: (−2,4)
3. C: (−5,−1)
4. D: (3,−2)