If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: High school geometry>Unit 6

Lesson 1: Distance and midpoints

# Midpoint formula

Learn how to use the midpoint formula to find the midpoint of a line segment on the coordinate plane, or find the endpoint of a line segment given one point and the midpoint. Created by Sal Khan.

## Want to join the conversation?

• How do you answer a problem using the midpoint formula when you are only given one end point and the midpoint?
• I don't think you need the answer 11 years later, but I'll still answer 😁

If we are given 1 endpoint and the midpoint, then we use the reverse of the midpoint theorem.
Say we have the endpoint as (0,0) and the midpoint as (3,1).
Then we would graph it as: (0,0) --- (3,1) --- (X,Y)

To Solve X:
∴ ½ ( x of point A + what we are solving for) = x of midpoint
= ½ (0 + X) = 3
= 0 + X = 3 x2
∴ X = 6

To Solve Y:
∴ ½ ( y of point A + what we are solving for) = y of midpoint
= ½ (0 + Y) = 1
= 0 + Y = 1 x2
∴ Y = 2

∴ The other endpoint = (6,2)
• Instead of finding the mean, can you find the median?
• With only two data points, the mean, median and mode are all the same.
• This helped a lot more! However, I'm still confused. Math isn't my thing. I understand stuff better, visually. I don't understand how the mean works. I used to know what an average was all through out elementary, but when we learned this on Friday, I was suddenly confused.
When you count the half way point of the x values, you get 4.5. That's the median/mean. When the mid point equation was created, did someone notice that the median was the same as the mean so they came up with that equation to make life easy? If not, then what does "mean" actually mean. I know how to get it, i know it's the average .. but what is the average,central number or mean of a set of numbers supposed to be?
• Simply defined; A median is a number that is between two numbers which is exactly halfway, like for example; the median of 3 and 5 is 4 (There are many numbers between 3 and 5...but 4 is the median because the difference between 3 and 4 is the same as the difference between 4 and 5) So if you take on the number line, the median of 3 and 5 must be equidistant from both 3 and 5. The formula for finding out the median is the sum of those two numbers divided by two. [ie. (a+b)/2, where a and b are numbers for whom you want to find the median] Here's how it works; Suppose you have a line segment on the number line with start point 3 and end point 5,the midpoint of the segment is 4. We know that point 4 is equidistant from both ends of the segment, but in general we can also find out the length of our segment and divide it by two to find the length between the median and each of the end points...our line segments length is 2 units, (since it starts at 3 and ends at 5) and if we wanted to find the midpoint of the segment, you can simply divide its length into halves and add the value to 3 (just try it on paper!) If we use the formula for median; then its (3+5)/2, we also get 4, but why this works?
The difference between 3 and 5 is 2, so both numbers can be represented as 3 and (3+2), so in our previous way, we divided the distance by two and added it to the start point, and that's exactly what the formula does...we have added 3 and (3+2) together and divided by two, that is [(3+3)+(2)]/2...notice that the difference between the numbers is getting divided by two and also 3 is repeated two times in the numerator!
• What is average actually?I don't understand difference between mean media mode either
• Take, for example, the numbers 1, 2, 3, 4, and 5.

Average: Add all the numbers together and divide them by 5(because there are 5 numbers that we added together).

1+2+3+4+5 = 15
15/5 = 3

The average of these numbers is 3.
"Mean" is basically just another word for the average.

"Median" is the middle number in a list of numbers that are ordered from least to greatest. In our example set of numbers, the median would also be 3.

"Mode" is the most frequent number. For instance, if you have the numbers 1, 2, 3, 4, 4, and 5, the number 4 would be the mode or most frequent number.

See this video:

Hope this helps!
• Hey Sal, isn't the midpoint formula (x1 +x2 / 2), (y1 + y2 / 2?)
• This is the formula he uses in the video, but he just simplifies it. x+1/2 is the same thing as the average or mean, and the same goes for the y coordinate.
(1 vote)
• How do you know which number to put in first? The formula is (x1+x2)/2 + (y1+y2)/2, but how do you know which number should be put in x1? Could I just put either of the x-values? I understand all of the distance formula except for this part.
• Addition is commutative, so it doesn't matter here.

Generally, these subscripts serve to group an x/y pair as a point and as long as you use the corresponding x/y pair it does not matter which pair is designated 1 or 2.
• Would finding the hypotenuse and then dividing by 2 also work?
• Yeah, but it's essentially just adding an extra step to what you are already doing. plus you would need extra steps to find the x and y coordinates
(1 vote)
• How to find Endpoint

Point A- (-7,-9)
Midpoint- (-0.5, -3)
Point B- (?) - (6,3)

How to find x:

1/2 (-7+x)= -0.5
-3.5 + 1/2x= -0.5
+3.5 +3.5

1/2x = 3
1/2 12
*you divide both sides and eliminate one with the x 1/2 and just divide 3 divided by 1/2

x= 6

You find Y by doing the same just put the coordinates of Y

• How do u find the answer to questions like: The point (7,−2) is the midpoint of (6,−6) and what point?
(1 vote)
• 7=1/2(6+x) => 2(7)=6+x => 14=6+x => 8=x
-2=1/2(-6+y) => 2(-2)=-6+y => -4=-6+y => 2=y
therefore the other point would be (8,2)