A coordinate plane consists of two number lines that intersect at zero on both lines, as shown below.
The horizontal number line is called the -axis, and the vertical number line is the -axis.
The point of intersection of the two lines is called the origin and is labeled
An ordered pair is a collection of two numbers shown with parentheses. Some examples of ordered pairs are:
Every point in the coordinate plane can be represented using an ordered pair, and we use an ordered pair to plot a point.
For example, let's see how to plot the point .
Starting at the origin:
- The first number tells us to move units along the -axis
- The second number tells us to move units up.
And that's it! We have successfully plotted the point.
Each number in the ordered pair has a special name:
The first number is called the -coordinate.
The second number is called the -coordinate.
So in the point the -coordinate is and the -coordinate is .
Important! The coordinates of the origin are
What is missing in the following sentence?
In the coordinate plane, the vertical number line is called the
In the coordinate plane, the vertical number line is called the -axis.
What is missing in the following sentence?
In the coordinate plane, the point of intersection of the $x$-axis and $y$-axis is called the $\underline{\phantom{{}^{0000000000000000000}}}.$
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a
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ordered pair |
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b
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origin |
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c
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vertex |
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d
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$y$-coordinate |
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e
|
$x$-coordinate |
What is missing in the following sentence?
In the coordinate plane, the horizontal number line is called the $\underline{\phantom{{}^{0000000000000000000}}}.$
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a
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origin |
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b
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$y$-coordinate |
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c
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$y$-axis |
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d
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$x$-coordinate |
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e
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$x$-axis |
What is the -coordinate of the point
To find the -coordinate of the point we start at the origin, move units right (along the -axis) and then units up (along the -axis). Therefore, the -coordinate is
So the coordinates of are Therefore, the -coordinate is
What are the coordinates of the point $B?$
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a
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$(6,4)$ |
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b
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$(0,6)$ |
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c
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$(10,4)$ |
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d
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$(4,6)$ |
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e
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$(4,0)$ |
What is the $y$-coordinate of the point $P?$
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a
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$\sqrt 3$ |
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b
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$1$ |
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c
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$2$ |
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d
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$0$ |
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e
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$3$ |
What is missing in the following sentence?
To graph the point in the coordinate plane, start at the origin and move
The -coordinate is zero. Therefore, we do not need to move along the -axis to plot the point. We only need to move along the -axis.
So, to graph the point , we start at the origin and move units up.
What is missing in the following sentence?
To graph the point $(2,0)$ in the coordinate plane, start at the origin and move $\underline{\phantom{{}^{0000000000000000000}}}.$
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a
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$2$ units right, then $2$ units up |
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b
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$2$ units left, then $2$ units up |
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c
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$2$ units right |
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d
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$2$ units left |
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e
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$2$ units up |
What is missing in the following sentence?
To graph the point $(0,3)$ in the coordinate plane, start at the origin and move $\underline{\phantom{{}^{0000000000000000000}}}.$
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a
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$3$ units right, then $3$ units up |
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b
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$3$ units left, then $3$ units up |
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c
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$3$ units up |
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d
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$3$ units right |
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e
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$3$ units left |
Sometimes, we might want to call the coordinate axes by different names.
For example, if we wanted to compare price vs. time, it's more convenient to label our axes and as shown below:
In this case, the horizontal axis is called the -axis, and the vertical axis is called the -axis.
If we're given an ordered pair, for example in this coordinate plane, the number is the -coordinate and the number is the -coordinate.
It's important to realize that we can call the axes whatever we want. However, and are the most common names that we use.
What is the -coordinate of the point
To get to point we start at the origin, move units right (along the -axis) and then units up (along the -axis).
So the coordinates of are Therefore, the -coordinate is
What is the $t$-coordinate of the point $A?$
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a
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$2$ |
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b
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$8$ |
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c
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$0$ |
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d
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$3$ |
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e
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$5$ |
What is the $r$-coordinate of the point $A?$
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a
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$0$ |
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b
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$4$ |
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c
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$2$ |
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d
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$3$ |
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e
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$6$ |
