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Question 84566: what is the midpoint between (-7,2) and (3,0)? i tried using the midpoint formula, but i still cannot figure out the right answer.
thanks for your help
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the two points (-7, 2) and (3,0). Find the midpoint.
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The x value of the midpoint is halfway between the two x values for the end points. In
other words, the x value of the midpoint is halfway between -7 and +3 on the number line.
You can get this by calculating the distance between -7 and +3. The distance is 10 units
(you can count this out by plotting -7 and +3 on the number line and then counting the
number of units between the two points. You will see that it is 10 units. Half of that
length is 10/2 or 5 units. Therefore the halfway point between -7 and +3 lies either 5
units to the right of -7 or 5 units to the left of +3. In either case the midpoint
between these values is at -2. Since we were working with the x values, we can now say
that the x value of the midpoint is -2.
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Another way we could have gotten the x value of the midpoint is to just average the x
values of the two given end points. In other words, average -7 and +3. Do this by adding
them together and dividing them by 2:
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Averaging ... (-7 + 3)/2 = -4/2 = -2.
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This agrees with what we found on the number line by counting up 5 from -7 or down 5 from
+3.
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So we now know that the x value of the midpoint is -2.
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Next we need to find the y value of the midpoint. The y values of the two given endpoints
are 2 and 0. There are 2 units of difference between them. So halfway between them is
1 unit. This means that the midpoint between them is 1 less than 2 or 1 more than zero.
This means that the y value of the midpoint is +1.
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We could also have gotten this result by averaging the y values of the 2 endpoints.
In other words, averaging +2 and 0. Add them together and divide by 2:
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(2 + 0)/2 = 2/2 = 1
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That's all there is to it. The x value for the midpoint is -2 and the y value for the
midpoint is +1 so the midpoint is given by (-2, +1)
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Hope this helps you to see how to get the midpoint for this problem.
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