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,
and
the midpoint formula states how to find the coordinates of the midpoint
A graphical view of a midpoint is shown in
[link] . Notice that the line segments on either side of the midpoint are congruent.
Finding the midpoint of the line segment
Find the midpoint of the line segment with the endpoints
and
Use the formula to find the midpoint of the line segment.
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.
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy....
I have so many questions in mind ....
all of scientists of the word they just give opinion only.
but they never think true or false ...
i respect all of them...
I believes whole universe depending
on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*).
So it would just barely creep over the horizon.
Christopher
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