Cartesian Coordinate System
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Pre-Calculus › Cartesian Coordinate System
The point is in which quadrant?
III
I
II
IV
Lies on an axis
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.
The point is in which quadrant?
III
I
II
IV
Lies on an axis
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.
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
.
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
.
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
.
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
.
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.
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.
Which of the following does not lie on the line given by the equation below?
Explanation
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.
Which of the following does not lie on the line given by the equation below?
Explanation
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.