How do you find the endpoint of a line when you are given the other endpoint and the midpoint?

Great question, and it's definitely a situation we need to be able to solve. When we are *given the Midpoint and an Endpoint, and asked to find the _Other Endpoint*_. We can still *use the concepts from the Midpoint Formula* _by plugging in the information we do have_, because… we normally _find the Midpoint_ by adding the corresponding coordinates, then dividing by two… (first endpoint + second endpoint) divided by two = Midpoint So, we know that… (*x1 + x2)/2 = Midpoint x* and that… (*y1 + y2)/2 = Midpoint y* *the given Endpoint (x, y) can be plugged into _either the first or second_ x and y* locations because addition is Commutative, (it's rearrangeable), so it doesn't matter which end values are first or second, and *the given Midpoint, (x or y), is placed as equal* to the Endpoint addition then division. Given: *Endpoint (3, 5) Midpoint (7, 10*) •Find _Other_ Endpoint = (x1 + x2)/2 = Midpoint x and (y1 + y2)/2 = Midpoint y = (*x + 3)/2 = 7* and (*y + 5)/2 = 10* •Let's solve for x first: (*x + 3)/2 = 7* _Multiply both sides by 2_, to cancel the division on the left. = *2*((x + 3)/2) = 7 • *2* = *x + 3 = 14* _Subtract 3 from both sides_, to isolate x on the left. = x + 3 -3 = 14 -3 = *x = 11* ←🥳 •Solve for y the same way… (*y + 5)/2 = 10* = 2((y + 5)/2) = 10(2) = *y + 5 = 20* = *y = 20 -5* = *y = 15* ←🥳 • Other Endpoint is at: (*11, 15*) ←🥳🥳 •Each time the pattern of operations _will be the same_: _*Multiply_ the Midpoint coordinate by 2, then _add or subtract_ the given Endpoint* to isolate variable. *2 • (Midpoint x or y) +/- (endpoint) = other endpoint* •Be aware if a given Endpoint *coordinate is negative, it will be added* rather than subtracted to isolate the variable. (*Example in Comments*) (ㆁωㆁ)I hope this helps someone!

don't u divied when u do the midpoint

You are finding the average, so one way is to add the two x coordinates and divide by 2, then do the same for the y coordinates.

how do i find coordinators if im looking for the endpoint

Are you saying you know one endpoint and the midpoint? If this is what you are asking, find the vector from the endpoint to the midpoint, the starting at midpoint, go along an equivalent vector. For example, endpoint is at (5,6) and midpoint is at (3,8) so the vector is <3-5, 8-6> or <-2,2>. SO starting at (3,8) along vector <-2,2), you end at (1,10).

what is length triangle mean?

it means what is the length of the triangle

lowkey brain screaming - im still somewhat confused

The midpoint formula is just an average. Add the 2 X-values, then divide by 2. Add the 2 Y-values, then divide by 2. You have then found the average for the X and Y values which gives you the point half way between the original 2 points.

to get a good run for its money solve (3,-5) and (-8,6) by using the Distance formula: D = (x2-x1)^2 + (y2-y1)^2

Your formula for distance is incorrect. You forgot that you need to take the square root of the entire right side. D = sqrt[(x2-x1)^2 + (y2-y1)^2]

Main content

Geometry (all content)

Course: Geometry (all content) > Unit 15

Lesson 1: Distance and midpoints

Midpoint formula review

Q: what is length triangle mean?

it means what is the length of the triangle

Q: lowkey brain screaming - im still somewhat confused

The midpoint formula is just an average. Add the 2 X-values, then divide by 2. Add the 2 Y-values, then divide by 2. You have then found the average for the X and Y values which gives you the point half way between the original 2 points.

Q: to get a good run for its money solve (3,-5) and (-8,6) by using the Distance formula: D = (x2-x1)^2 + (y2-y1)^2

Your formula for distance is incorrect. You forgot that you need to take the square root of the entire right side. D = sqrt[(x2-x1)^2 + (y2-y1)^2]

CCSS.Math:

HSG.GPE.B.6

Google Classroom

Review the midpoint formula and how to apply it to solve problems.

What is the midpoint formula?

The formula gives the midpoint of the points left parenthesis, start color #1fab54, x, start subscript, 1, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 1, end subscript, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, x, start subscript, 2, end subscript, end color #1fab54, comma, start color #e07d10, y, start subscript, 2, end subscript, end color #e07d10, right parenthesis in the coordinate plane:

left parenthesis, start color #1fab54, start fraction, x, start subscript, 1, end subscript, plus, x, start subscript, 2, end subscript, divided by, 2, end fraction, end color #1fab54, comma, start color #e07d10, start fraction, y, start subscript, 1, end subscript, plus, y, start subscript, 2, end subscript, divided by, 2, end fraction, end color #e07d10, right parenthesis

Want to learn more about the midpoint formula? Check out this video.

What problems can I solve with the midpoint formula?

Given two points on the plane, you can find their midpoint. For example, let's find the midpoint of left parenthesis, start color #1fab54, 5, end color #1fab54, comma, start color #e07d10, 3, end color #e07d10, right parenthesis and left parenthesis, start color #1fab54, 1, end color #1fab54, comma, start color #e07d10, 7, end color #e07d10, right parenthesis:

\begin{aligned} &\phantom{=}\left(\greenD{\dfrac{x_1+x_2}{2}}, \goldD{\dfrac{y_1+y_2}{2}}\right) \\\\ &=\left(\greenD{\dfrac{5+1}{2}}, \goldD{\dfrac{3+7}{2}}\right)\quad\small\gray{\text{Plug in coordinates}} \\\\ &=(\greenD3, \goldD5) \end{aligned}

Notice: we were careful to put the x-coordinates together and the y-coordinates together and not mix them up.

Check your understanding

Problem 1

Current

What is the midpoint of left parenthesis, 6, comma, 2, right parenthesis and left parenthesis, 10, comma, 0, right parenthesis?

(Choice A)
left parenthesis, 8, comma, 1, right parenthesis
(Choice B)
left parenthesis, 4, comma, 5, right parenthesis
(Choice C)
left parenthesis, 1, comma, 8, right parenthesis
(Choice D)
left parenthesis, 5, comma, 4, right parenthesis

Want to try more problems like this? Check out this exercise.

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mohnzy02
Posted 6 years ago. Direct link to mohnzy02's post “How do you find the endpo...”
How do you find the endpoint of a line when you are given the other endpoint and the midpoint?
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(15 votes)
Answer
- Seed Something
  Posted a year ago. Direct link to Seed Something's post “Great question, and it's ...”
  Great question, and it's definitely a situation we need to be able to solve.
  
  When we are given the Midpoint and an Endpoint, and asked to find the Other Endpoint.
  
  We can still use the concepts from the Midpoint Formula by plugging in the information we do have, because…
  
  we normally find the Midpoint by adding the corresponding coordinates, then dividing by two…
  
  (first endpoint + second endpoint) divided by two = Midpoint
  
  So, we know that…
  (x1 + x2)/2 = Midpoint x
  and that…
  (y1 + y2)/2 = Midpoint y
  
  the given Endpoint (x, y) can be plugged into either the first or second x and y locations because addition is Commutative, (it's rearrangeable), so it doesn't matter which end values are first or second,
  
  and the given Midpoint, (x or y), is placed as equal to the Endpoint addition then division.
  
  Given:
  Endpoint (3, 5)
  Midpoint (7, 10)
  
  •Find Other Endpoint
  =
  (x1 + x2)/2 = Midpoint x
  and
  (y1 + y2)/2 = Midpoint y
  =
  (x + 3)/2 = 7
  and
  (y + 5)/2 = 10
  
  •Let's solve for x first:
  (x + 3)/2 = 7
  Multiply both sides by 2,
  to cancel the division on the left.
  =
  2((x + 3)/2) = 7 • 2
  =
  x + 3 = 14
  Subtract 3 from both sides,
  to isolate x on the left.
  =
  x + 3 -3 = 14 -3
  =
  x = 11 ←🥳
  
  •Solve for y the same way…
  (y + 5)/2 = 10
  =
  2((y + 5)/2) = 10(2)
  =
  y + 5 = 20
  =
  y = 20 -5
  =
  y = 15 ←🥳
  
  • Other Endpoint is at:
  (11, 15) ←🥳🥳
  
  •Each time the pattern of operations will be the same:
  Multiply the Midpoint coordinate by 2, then add or subtract the given Endpoint to isolate variable.
  
  2 • (Midpoint x or y) +/- (endpoint)
  =
  other endpoint
  
  •Be aware if a given Endpoint coordinate is negative, it will be added rather than subtracted to isolate the variable.
  
  (Example in Comments)
  
  (ㆁωㆁ)I hope this helps someone!
  Comment on Seed Something's post “Great question, and it's ...”
  (20 votes)
windham.brenaisha
Posted 5 years ago. Direct link to windham.brenaisha's post “don't u divied when u do ...”
don't u divied when u do the midpoint
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(5 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “You are finding the avera...”
  You are finding the average, so one way is to add the two x coordinates and divide by 2, then do the same for the y coordinates.
  Button navigates to signup page
  (14 votes)
Justice Clark
Posted 5 years ago. Direct link to Justice Clark's post “how do i find coordinator...”
how do i find coordinators if im looking for the endpoint
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(3 votes)
Answer
- David Severin
  Posted 5 years ago. Direct link to David Severin's post “Are you saying you know o...”
  Are you saying you know one endpoint and the midpoint? If this is what you are asking, find the vector from the endpoint to the midpoint, the starting at midpoint, go along an equivalent vector. For example, endpoint is at (5,6) and midpoint is at (3,8) so the vector is <3-5, 8-6> or <-2,2>. SO starting at (3,8) along vector <-2,2), you end at (1,10).
  Button navigates to signup page
  (9 votes)
Ella Mae Latinah Alvior
Posted 6 years ago. Direct link to Ella Mae Latinah Alvior's post “formula for the length of...”
formula for the length of scalene triangle
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(1 vote)
Answer
ni064941
Posted 3 years ago. Direct link to ni064941's post “what is length triangle m...”
what is length triangle mean?
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(2 votes)
Answer
- josh
  Posted 3 years ago. Direct link to josh's post “it means what is the leng...”
  it means what is the length of the triangle
  Button navigates to signup page
  (5 votes)
K.B
Posted a year ago. Direct link to K.B's post “lowkey brain screaming - ...”
lowkey brain screaming - im still somewhat confused
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(1 vote)
Answer
- Kim Seidel
  Posted a year ago. Direct link to Kim Seidel's post “The midpoint formula is j...”
  The midpoint formula is just an average.
  Add the 2 X-values, then divide by 2.
  Add the 2 Y-values, then divide by 2.
  You have then found the average for the X and Y values which gives you the point half way between the original 2 points.
  Comment on Kim Seidel's post “The midpoint formula is j...”
  (6 votes)
miquitaia
Posted 4 years ago. Direct link to miquitaia's post “How do you find the value...”
How do you find the values of a and b when given the endpoints (1,a) and (b,-4) and the midpoint (4,-6)?
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(3 votes)
Answer
Jason Duran
Posted 6 years ago. Direct link to Jason Duran's post “Plot two points to find m...”
Plot two points to find me square in the above graph. Label the points R and S. A square is a quadrilateral with all for size of the same length. After planting the points trace to square by connecting the points
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(2 votes)
Answer
Tenzin
Posted 2 years ago. Direct link to Tenzin's post “how do you find the midpo...”
how do you find the midpoint of 3 coordinates
Button navigates to signup pageComment on Tenzin's post “how do you find the midpo...”
(2 votes)
Answer
Calob .A. Lewis
Posted 4 months ago. Direct link to Calob .A. Lewis's post “to get a good run for its...”
to get a good run for its money solve (3,-5) and (-8,6) by using the Distance formula:
D = (x2-x1)^2 + (y2-y1)^2
Button navigates to signup pageButton navigates to signup page
(1 vote)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “Your formula for distance...”
  Your formula for distance is incorrect. You forgot that you need to take the square root of the entire right side.
  D = sqrt[(x2-x1)^2 + (y2-y1)^2]
  Comment on Kim Seidel's post “Your formula for distance...”
  (3 votes)