Good Day! What if the given are the other endpoint and the midpoint? How do you get the coordinates of the other endpoint?

I believe you would simply find the differences in x and y from the midpoint to the one endpoint, multiply them by two (giving yourself the two side lengths of a right triangle, if you choose to think about your two points in that way), and add these displacements to your given endpoint.

How would you solve a problem in which you do not know point B but are given the midpoint and point A?

Here's what I did when I first learned Geometry 50 years ago. I ask myself, * How much did I move in what direction from point A to the MIDPOINT. * Make the same movement in the same directions to find point B. For example, if point A is at (3,2) and the midpoint is at (-2,5), i would move 5 left and 3 up from A to M. Do the same thing again. Move 5 left and 3 up from M and you will find yourself at B.

the line y=x and the curve y=4x-x^2 intersect at the point p and q. find the co-ordinates of p and q

Substitute for y to get x = 4x - x^2 then move everything to one side, factor, and solve. Try it and if you still need help, ask again.

Why do we add instead of subtract the numbers

You basically are averaging the X and Y values. Consider if you had a grade of 60 and a grade of 100, how would you find the grade that is halfway between them? You would average them. The Midpoint Formula does the same thing. If one X-value is at 2 and the other X-value is at 8, to find the X-value halfway between them, you add 2+8 and divide by 2 = 5. Your would repeat the process for the Y-values to find the Y-coordinate of the midpoint.

It doesn't tell us how to solve for when you have one point and the midpoint... what do you do for that? Because it only shows solving for the midpoint, but what if you're solving for the other point on the line?

Copy from Kim Seidel's answer: Find the change in Y and change in X between that 2 points that you have. Your point b will be on the opposite side of the midpoint from point a. And it will have the same change in Y and change in X. For example: If a = (2,5) and the midpoint = (-1,3): Change in Y = 5-3 = 2 Change in X = 2-(-1) = 3 Point a is to the right of the midpoint. So point b must be to the left. So, we move in the opposite direction from the midpoint. To go left, we need to change the values to negatives. y-value of b = 3-2 = 1 x-value of b = -1-3 = -4 b = (-4,1)

I am so confused but okay

The midpoint formula is basically an average. You add the two x-values and divide by 2. You add the two y-values and divide by 2. This gives you the coordinates of the midpoint (the point located half-way between the original two points).

how do you find the other point if you know one of the points plus the mid point

You set up an equation. Here's an example with just the x-coordinate. I believe you can expand this to the y-coordinate. Let the mid point x-coordinate be m, and the two points be x1 and x2. (x1+x2)/2 = m x1+x2 = 2m *x2 = 2m - x1*

do u guys think this is easy? is this the easiest thing in geometry, im trying to learn b4 i go to school.

I think that any math that involves a formula is easy.

Main content

High school geometry

Course: High school geometry > Unit 6

Lesson 1: Distance and midpoints

Midpoint formula

Google Classroom

Walk through writing a general formula for the midpoint between two points.

The start color #11accd, start text, m, i, d, p, o, i, n, t, end text, end color #11accd 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 is given by the following formula:

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

In this article, we're going to derive this formula!

Deriving the midpoint formula

Let's start by plotting 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.

The start color #11accd, start text, m, i, d, p, o, i, n, t, end text, end color #11accd is the point halfway between each of the points:

An expression for the x-coordinate of the start color #11accd, start text, m, i, d, p, o, i, n, t, end text, end color #11accd is 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:

[Why does this expression work?]

Similarly, an expression for the y-coordinate of the start color #11accd, start text, m, i, d, p, o, i, n, t, end text, end color #11accd is start color #e07d10, 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, end color #e07d10:

That's it! We derived the following formula for the start color #11accd, start text, m, i, d, p, o, i, n, t, end text, end color #11accd!

Interestingly, a lot of people don't memorize this exact formula. Instead, they remember that to find the midpoint, you take the average of the x-coordinates and the average of the y-coordinates.

Practice problem

Point start color #6495ed, A, end color #6495ed is at start color #6495ed, left parenthesis, minus, 6, comma, 8, right parenthesis, end color #6495ed and point start color #28ae7b, B, end color #28ae7b is at start color #28ae7b, left parenthesis, 6, comma, minus, 7, right parenthesis, end color #28ae7b.

What is the midpoint of line segment start overline, A, B, end overline?

left parenthesis

right parenthesis

[Show solution]

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Alexene Faith S. Tomate
Posted 7 years ago. Direct link to Alexene Faith S. Tomate's post “Good Day! What if the giv...”
Good Day! What if the given are the other endpoint and the midpoint? How do you get the coordinates of the other endpoint?
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(35 votes)
Answer
- Stephen
  Posted 3 years ago. Direct link to Stephen's post “I believe you would simpl...”
  I believe you would simply find the differences in x and y from the midpoint to the one endpoint, multiply them by two (giving yourself the two side lengths of a right triangle, if you choose to think about your two points in that way), and add these displacements to your given endpoint.
  Button navigates to signup page
  (14 votes)
Jade Slowik
Posted 7 years ago. Direct link to Jade Slowik's post “How would you solve a pro...”
How would you solve a problem in which you do not know point B but are given the midpoint and point A?
Button navigates to signup pageButton navigates to signup page
(16 votes)
Answer
- John Williamson
  Posted 7 years ago. Direct link to John Williamson's post “Here's what I did when I ...”
  Here's what I did when I first learned Geometry 50 years ago.
  
  I ask myself,
  
  * How much did I move in what direction from point A to the MIDPOINT.
  
  * Make the same movement in the same directions to find point B.
  
  For example, if point A is at (3,2) and the midpoint is at (-2,5), i would move 5 left and 3 up from A to M.
  
  Do the same thing again. Move 5 left and 3 up from M and you will find yourself at B.
  Comment on John Williamson's post “Here's what I did when I ...”
  (30 votes)
Humble Child Pööťý
Posted 6 years ago. Direct link to Humble Child Pööťý's post “the line y=x and the curv...”
the line y=x and the curve y=4x-x^2 intersect at the point p and q. find the co-ordinates of p and q
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- David Severin
  Posted 6 years ago. Direct link to David Severin's post “Substitute for y to get x...”
  Substitute for y to get x = 4x - x^2 then move everything to one side, factor, and solve. Try it and if you still need help, ask again.
  Button navigates to signup page
  (8 votes)
Alexene Faith S. Tomate
Posted 7 years ago. Direct link to Alexene Faith S. Tomate's post “Let's say for example, po...”
Let's say for example, points A and B are divided into four points. How do you get the coordinate of each point?
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(5 votes)
Answer
Jonathan Huang
Posted 7 years ago. Direct link to Jonathan Huang's post “Why do we add instead of ...”
Why do we add instead of subtract the numbers
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(6 votes)
Answer
- Kim Seidel
  Posted 7 years ago. Direct link to Kim Seidel's post “You basically are averagi...”
  You basically are averaging the X and Y values.
  Consider if you had a grade of 60 and a grade of 100, how would you find the grade that is halfway between them? You would average them. The Midpoint Formula does the same thing.
  If one X-value is at 2 and the other X-value is at 8, to find the X-value halfway between them, you add 2+8 and divide by 2 = 5.
  Your would repeat the process for the Y-values to find the Y-coordinate of the midpoint.
  Comment on Kim Seidel's post “You basically are averagi...”
  (6 votes)
XxGl1tchxX
Posted a month ago. Direct link to XxGl1tchxX's post “It doesn't tell us how to...”
It doesn't tell us how to solve for when you have one point and the midpoint... what do you do for that? Because it only shows solving for the midpoint, but what if you're solving for the other point on the line?
Button navigates to signup pageComment on XxGl1tchxX's post “It doesn't tell us how to...”
(6 votes)
Answer
- Derrick
  Posted a month ago. Direct link to Derrick's post “Copy from Kim Seidel's an...”
  Copy from Kim Seidel's answer:
  
  Find the change in Y and change in X between that 2 points that you have. Your point b will be on the opposite side of the midpoint from point a. And it will have the same change in Y and change in X. For example:
  
  If a = (2,5) and the midpoint = (-1,3):
  Change in Y = 5-3 = 2
  Change in X = 2-(-1) = 3
  Point a is to the right of the midpoint. So point b must be to the left. So, we move in the opposite direction from the midpoint. To go left, we need to change the values to negatives.
  y-value of b = 3-2 = 1
  x-value of b = -1-3 = -4
  b = (-4,1)
  Button navigates to signup page
  (4 votes)
baskarsandra
Posted 7 years ago. Direct link to baskarsandra's post “do u guys think this is e...”
do u guys think this is easy? is this the easiest thing in geometry, im trying to learn b4 i go to school.
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kendra Wilson
  Posted 7 years ago. Direct link to Kendra Wilson's post “I think that any math tha...”
  I think that any math that involves a formula is easy.
  Button navigates to signup page
  (10 votes)
26jamiras614
Posted 4 months ago. Direct link to 26jamiras614's post “I am so confused but okay”
I am so confused but okay
Button navigates to signup pageComment on 26jamiras614's post “I am so confused but okay”
(4 votes)
Answer
- Kim Seidel
  Posted 4 months ago. Direct link to Kim Seidel's post “The midpoint formula is b...”
  The midpoint formula is basically an average. You add the two x-values and divide by 2. You add the two y-values and divide by 2. This gives you the coordinates of the midpoint (the point located half-way between the original two points).
  Button navigates to signup page
  (4 votes)
chloe johnson
Posted 6 months ago. Direct link to chloe johnson's post “Hi, i was wondering were ...”
Hi, i was wondering were i could find "how to find one of the endpoints given one endpoint and the midpoint"
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(5 votes)
Answer
- Aristotle
  Posted 3 months ago. Direct link to Aristotle's post “Look at each pair of coor...”
  Look at each pair of coordinates (x, y) and then the other pair of coordinates, 2nd pair(x,y).
  
  now add both the x's and divide by two. (Example: x1+x2/2 = x-midpoint coordinate)
  
  take your answer for that and write it in the first column (here, )
  
  now add the y's and divide by two. (Example: y1+y2/2 = y-midpoint coordinate)
  
  now take that answer and write it in the second column( ,here)
  
  Finally, put the two together and you should have your MIDPOINT. Woo! (x-midpoint, y-midpoint) = the midpoint between the two coordinates you were given in the problem to solve.
  this should help!
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  (1 vote)
makennak921
Posted 3 months ago. Direct link to makennak921's post “how do you find the other...”
how do you find the other point if you know one of the points plus the mid point
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(3 votes)
Answer
- joshua
  Posted 3 months ago. Direct link to joshua's post “You set up an equation. H...”
  You set up an equation. Here's an example with just the x-coordinate. I believe you can expand this to the y-coordinate.
  Let the mid point x-coordinate be m, and the two points be x1 and x2.
  (x1+x2)/2 = m
  x1+x2 = 2m
  x2 = 2m - x1
  Button navigates to signup page
  (4 votes)