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.
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?