Precalculus : Cartesian Coordinate System
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Example Questions
Example Question #1 : Plot Points
The point 
III
Lies on an axis
I
IV
II
III
In order to determine in which quadrant the point lies, we must remember the order of the quadrants. The first quadrant is that where x and y are both positive, to the upper right of the origin. To move sequentially to the final quadrant, we go counterclockwise from the first quadrant, which means the second is where x is negative and y is positive, the third is where x and y are both negative, and the fourth is where x is positive and y is negative. We can see from our point (-3,-8) that x and y are both negative, which means the point lies in the third quadrant.
Example Question #2 : Cartesian Coordinate System
Use the distance formula to find the length of 
Since the length of 
Thus, the area of the circle is
Example Question #1 : Plot Points
Which of the following coordinates does NOT fit on the graph of the corresponding function?
When looking at the graph, it is clear that when 
Therefore, at 
Example Question #4 : Plot Points
Which of the following 
When looking at the graph, it is clear that when 
Example Question #5 : Plot Points
Which of the following 
If we are to plug 
Therefore, we know that these coordinates do not lie on the graph of the function.
Example Question #2 : Cartesian Coordinate System
Which of the following 
If we were to plug in the coordinate 
Since these values do not equate properly when plugged into the function, we now know that 
Example Question #1 : Graph Equations
Given 
First, solve for 
Then, graph the 
Since the slope of the line is 
There is only one graph that fits these requirements.
Example Question #2 : Graph Equations
Which of the following does not lie on the line given by the equation below?
To determine if a point lies on a line, plug in the x-value and y-value to see if the equation is satisfied. We can do this for each choice to check.
For example:
Since both sides are equivalent, this point does lie on the line.
We can continue to do this for each of the points until one point does not work out.
Thus, this point does not lie on the line. Thus, this must be the solution.
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