<< Chapter < Page Chapter >> Page >

Using the midpoint formula

When the endpoints of a line segment are known, we can find the point midway between them. This point is known as the midpoint and the formula is known as the midpoint formula    . Given the endpoints of a line segment, ( x 1 , y 1 ) and ( x 2 , y 2 ) , the midpoint formula states how to find the coordinates of the midpoint M .

M = ( x 1 + x 2 2 , y 1 + y 2 2 )

A graphical view of a midpoint is shown in [link] . Notice that the line segments on either side of the midpoint are congruent.

This is a line graph on an x, y coordinate plane with the x and y axes ranging from 0 to 6. The points (x sub 1, y sub 1), (x sub 2, y sub 2), and (x sub 1 plus x sub 2 all over 2, y sub 1 plus y sub 2 all over 2) are plotted.  A straight line runs through these three points. Pairs of short parallel lines bisect the two sections of the line to note that they are equivalent.

Finding the midpoint of the line segment

Find the midpoint of the line segment with the endpoints ( 7 , −2 ) and ( 9 , 5 ) .

Use the formula to find the midpoint of the line segment.

( x 1 + x 2 2 , y 1 + y 2 2 ) = ( 7 + 9 2 , 2 + 5 2 ) = ( 8 , 3 2 )
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Find the midpoint of the line segment with endpoints ( −2 , −1 ) and ( −8 , 6 ) .

( 5 , 5 2 )

Got questions? Get instant answers now!

Finding the center of a circle

The diameter of a circle has endpoints ( −1 , −4 ) and ( 5 , −4 ) . Find the center of the circle.

The center of a circle is the center, or midpoint, of its diameter. Thus, the midpoint formula will yield the center point.

( x 1 + x 2 2 , y 1 + y 2 2 ) ( 1 + 5 2 , 4 4 2 ) = ( 4 2 , 8 2 ) = ( 2 , −4 )
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with the Cartesian coordinate system.

Key concepts

  • We can locate, or plot, points in the Cartesian coordinate system using ordered pairs, which are defined as displacement from the x- axis and displacement from the y- axis. See [link] .
  • An equation can be graphed in the plane by creating a table of values and plotting points. See [link] .
  • Using a graphing calculator or a computer program makes graphing equations faster and more accurate. Equations usually have to be entered in the form y= _____. See [link] .
  • Finding the x- and y- intercepts can define the graph of a line. These are the points where the graph crosses the axes. See [link] .
  • The distance formula is derived from the Pythagorean Theorem and is used to find the length of a line segment. See [link] and [link] .
  • The midpoint formula provides a method of finding the coordinates of the midpoint dividing the sum of the x -coordinates and the sum of the y -coordinates of the endpoints by 2. See [link] and [link] .

Section exercises

Verbal

Is it possible for a point plotted in the Cartesian coordinate system to not lie in one of the four quadrants? Explain.

Answers may vary. Yes. It is possible for a point to be on the x -axis or on the y -axis and therefore is considered to NOT be in one of the quadrants.

Got questions? Get instant answers now!

Describe the process for finding the x- intercept and the y -intercept of a graph algebraically.

Got questions? Get instant answers now!

Describe in your own words what the y -intercept of a graph is.

The y -intercept is the point where the graph crosses the y -axis.

Got questions? Get instant answers now!

When using the distance formula d = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 , explain the correct order of operations that are to be performed to obtain the correct answer.

Got questions? Get instant answers now!

Algebraic

For each of the following exercises, find the x -intercept and the y -intercept without graphing. Write the coordinates of each intercept.

y = −3 x + 6

The x- intercept is ( 2 , 0 ) and the y -intercept is ( 0 , 6 ) .

Got questions? Get instant answers now!

3 x 2 y = 6

The x- intercept is ( 2 , 0 ) and the y -intercept is ( 0 , −3 ) .

Got questions? Get instant answers now!

Questions & Answers

what does preconceived mean
sammie Reply
physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
why is communication effective
Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
Wekolamo Reply
please i need answer
Wekolamo
because it helps many people around the world to understand how to interact with other people and understand them well, for example at work (job).
Manix Reply
Agreed 👍 There are many parts of our brains and behaviors, we really need to get to know. Blessings for everyone and happy Sunday!
ARC
A child is a member of community not society elucidate ?
JESSY Reply
Isn't practices worldwide, be it psychology, be it science. isn't much just a false belief of control over something the mind cannot truly comprehend?
Simon Reply
compare and contrast skinner's perspective on personality development on freud
namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
Amesalu Reply
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
Zyryn Reply
good👍
Jonathan
and having a good philosophy of the world is like a sandwich and a peanut butter 👍
Jonathan
generally amnesi how long yrs memory loss
Kelu Reply
interpersonal relationships
Abdulfatai Reply
What would be the best educational aid(s) for gifted kids/savants?
Heidi Reply
treat them normal, if they want help then give them. that will make everyone happy
Saurabh
What are the treatment for autism?
Magret Reply
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities. before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue.. sometimes due to these physical problems..the diagnosis may be misdiagnosed. treatment for autism. well it depends on the severity. since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision. play therapy. speech therapy. Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game. string and beads game. the more you interact with the child the more effective
Jharna
results you'll get.. please consult a therapist to know what suits best on your child. and last as a parent. I know sometimes it's overwhelming to guide a special kid. but trust the process and be strong and patient as a parent.
Jharna
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask