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HEEEELP :] - Midpoint of a Line Segment

by cindy
(los angeles )










































Midpoint of a line Segment

The midpoint of a line segment is the point on the line which is exactly half way between the two end points.

What is the midpoint of a line segment with endpoints at (-4,15) and (22,3) ?

Comments for HEEEELP :] - Midpoint of a Line Segment

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Aug 01, 2012
Midpoint of a line Segment
by: Staff


Answer:


The MIDPOINT of a line segment is simply the AVERAGE of the “X” values and the AVERAGE of the “Y” values.


You can think of it like this:

The average of the two numbers, say 25 and 40, is the sum of the two numbers divided by 2.

Average of 25 and 40 = (25 + 40) / 2 = 32.5


Similarly, the average of the “x” values in your question is:

(x₁ + x₂) / 2

= (-4 + 22) / 2


= 18 / 2

= 9


The average of the “y” values in your question is:

(y₁ + y₂) / 2

= (15 + 3) / 2

= 18 / 2

= 9


>>> The midpoint of the line segment with endpoints at (-4,15) and (22,3):

midpoint = (9, 9)



The GENERAL FORMULA for the MIDPOINT of a line is:

Midpoint = [ (x₁ + x₂)/2 , (y₁ + y₂)/2]


If we apply the general formula to your question:

Midpoint = [ (x₁ + x₂)/2 , (y₁ + y₂)/2]

Midpoint = [(-4 + 22)/2, (15 + 3)/2]

Midpoint = [9, 9]

This is exactly the same answer we got originally.


Note that this formula works even if some of the values are negative values.

It also works with line segments that are entirely vertical, or horizontal.


The general formula will also work for a line in three dimensions.

In this case, the general formula will be:

Midpoint = [ (x₁ + x₂)/2 , (y₁ + y₂)/2, (z₁ + z₂)/2]



You can also use this formula to solve problems such as:


The midpoint of a line = (1.5, 4)

One of the end points is (-2, 0)

The “y” value of the other end point is not known: (5, y)

Find the second end point:

Midpoint (average) of “y” values = (y₁ + y₂)/2

(y₁ + y₂)/2 = 4

(0 + y₂)/2 = 4

y₂ = 8

the second end point is: (5, 8)




Thanks for writing.

Staff
www.solving-math-problems.com



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