# Precalculus : Cartesian Coordinate System

## Example Questions

### Example Question #1 : Cartesian Coordinate System

The point  is in which quadrant?

I

III

IV

Lies on an axis

II

III

Explanation:

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 : Plot Points

and  are located on the circle, with  forming its diameter. What is the area of the circle.

Explanation:

Use the distance formula to find the length of

.

Since the length of  is that of the diameter, the radius of the circle is .

Thus, the area of the circle is

.

### Example Question #3 : Plot Points

Which of the following coordinates does NOT fit on the graph of the corresponding function?

Explanation:

When looking at the graph, it is clear that when ,  has a value less than . If we were to plug in the value of , our equation would come out as such:

Therefore, at , we get a , providing the coordinate .

### Example Question #4 : Plot Points

Which of the following  coordinates does NOT correspond with the given function and graph?

Explanation:

When looking at the graph, it is clear that when ,  has a value greater than . When we plug in both  and  values into the function, it is clear that these values do not work for the function:

### Example Question #5 : Plot Points

Which of the following  coordinates does NOT correspond with the given function and graph?

Explanation:

If we are to plug  into our function, the values would not work and both sides of the equation would not be equal:

Therefore, we know that these coordinates do not lie on the graph of the function.

### Example Question #6 : Plot Points

Which of the following  coordinates does NOT correspond with the given function and graph?

Explanation:

If we were to plug in the coordinate  into the function, we will find that it does not equate properly:

Since these values do not equate properly when plugged into the function, we now know that  does not fit on the provided graph.

### Example Question #1 : Graph Equations

Given , which graph is the correct one?

Explanation:

First, solve for .

Then, graph the  at .

Since the slope of the line is , you can graph the point  as well.

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?