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Question 105880This question is from textbook Intermediate Algebra
: I don't know what I am doing wrong but I can't seem to get this right even using the solvers for this type problem.. Can someone please help me solve this before I pull out all my hair? Thank You.
I have to find the midpoint of this line segment;
P(2,8)
Q(5,8) Thanks.
This question is from textbook Intermediate Algebra
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the two points:
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P(2,8)
Q(5,8)
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The x-value of the midpoint of the line joining these two points is halfway between
the x-values of the two points. The two x-values are 2 and 5. Halfway between these
two values is 3.5. You can also find this by averaging the two x-values. The average
of 2 and 5 is found by adding these two values and dividing by 2. Averaging the two x
values for this problem is done this way:
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(2 + 5)/2 = 7/2 = 3.5
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The y-value of the midpoint of the line joining these two points is also halfway between
the y-values of the two points. The two y-values are 8 and 8. Halfway between these
two values is still 8 (since there is zero difference). You can also confirm this by
averaging the two y-values. The sum of the two y-values is 8 + 8 or 16. Divide this sum
by 2 to get the average y-value as 16/2 = 8.
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So the midpoint of the line that connects the two given points is (3.5, 8).
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In general, if you are given any two points and asked to find the midpoint of the line
joining them, you get the x-value of the midpoint by averaging the x-values of the two
points. And you find the y-value of the midpoint by averaging the y-values of the two
points.
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In this problem the two points have the same y-value. This means that the line connecting
the points is a horizontal line that runs between the x-values 2 and 5. So the midpoint
is just halfway along this horizontal line. This verifies that to be on the line, the
y-value of the midpoint must be 8. And the x-value must be halfway between x= 2 and x = 5.
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Again, in summary the midpoint of the line joining the given points is (3.5, 8).
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Hope this explains the process of finding midpoints of lines joining two given points.
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