• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

Midpoint of a Line Segment

December 4, 2020 by sastry

Midpoint of a Line Segment

The point halfway between the endpoints of a line segment is called the midpoint. A midpoint divides a line segment into two equal segments.
Midpoint of a Line Segment 1By definition, a midpoint of a line segment is the point on that line segment that divides the segment two congruent segments.
In Coordinate Geometry, there are several ways to determine the midpoint of a line segment.

Method 1:
If the line segments are vertical or horizontal, you may find the midpoint by simply dividing the length of the segment by 2 and counting that value from either of the endpoints.

Find the midpoints \(\overline { AB }\) and \(\overline { CD }\).
Midpoint of a Line Segment 2AB is 8 (by counting). The midpoint is 4 units from either endpoint. On the graph, this point is (1,4).
CD is 3 (by counting). The midpoint is 1.5 units from either endpoint. On the graph, this point is (2,1.5)

Method 2:
If the line segments are diagonally positioned, more thought must be paid to the solution. When you are finding the coordinates of the midpoint of a segment, you are actually finding the average (mean) of the x-coordinates and the average (mean) of the y-coordinates.

This concept of finding the average of the coordinates can be written as a formula:
Midpoint of a Line Segment 3NOTE: The Midpoint Formula works for all line segments: vertical, horizontal or diagonal.
Midpoint of a Line Segment 4

Consider this “tricky” midpoint problem:
M is the midpoint of \(\overline { CD }\). The coordinates M(-1,1) and C(1,-3) are given. Find the coordinates of point D.
First, visualize the situation. This will give you an idea of approximately where point D will be located. When you find your answer, be sure it matches with your visualization of where the point should be located.
Midpoint of a Line Segment 5
Midpoint of a Line Segment 6

Other Methods of Solution:
Verbalizing the algebraic solution:
Some students like to do these “tricky” problems by just examining the coordinates and asking themselves the following questions:
“My midpoint’s x-coordinate is -1. What is -1 half of? (Answer -2)
What do I add to my endpoint’s x-coordinate of +1 to get -2? (Answer -3)
This answer must be the x-coordinate of the other endpoint.”
These students are simply verbalizing the algebraic solution.
(They use the same process for the y-coordinate.)

Utilizing the concept of slope and congruent triangles:
A line segment is part of a straight line whose slope (rise/run) remains the same no matter where it is measured. Some students like to look at the rise and run values of the x and y coordinates and utilize these values to find the missing endpoint.

Find the slope between points C and M. This slope has a run of 2 units to the left and a rise of 4 units up. By repeating this slope from point M (move 2 units to the left and 4 units up), you will arrive at the other endpoint.
Midpoint of a Line Segment 7By using this slope approach, you are creating two congruent right triangles whose legs are the same lengths. Consequently, their hypotenuses are also the same lengths and DM = MC making M the midpoint of \(\overline { CD }\).

Filed Under: Mathematics Tagged With: Midpoint of a Line Segment

Primary Sidebar

  • MCQ Questions
  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC

Recent Posts

  • Air Pollution Essay for Students and Kids in English
  • 10 Lines on Satya Nadella for Students and Children in English
  • Essay on Wonders of Science | Wonders of Science for Students and Children in English
  • My Childhood Memories Essay | Essay on My Childhood Memories for Students and Children in English
  • Essay On Sports And Games | Sports And Games Essay for Students and Children in English
  • Clean India Slogans | Unique and Catchy Clean India Slogans in English
  • Animals that Start with Z | Listed with Pictures, List of Animals Starting with Z & Interesting Facts
  • Positive Words That Start With S | List of Positive Words Starting With S Meaning, Examples,Pictures and Facts
  • Positive Words that Start with B | List of 60 Positive Words Starting with B Pictures and Facts
  • Humanity Essay | Essay on Humanity for Students and Children in English
  • Teenage Pregnancy Essay | Essay on Teenage Pregnancy for Students and Children in English

Footer

  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • Picture Dictionary
  • English Speech
  • ICSE Solutions
  • Selina ICSE Solutions
  • ML Aggarwal Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Distance Education
DisclaimerPrivacy Policy
Area Volume Calculator