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.

The circumferences of two concentric circles differ by 10 inches. Compute the width of the ring between the two circles. Round off your answer to nearest hundredths place. send help thank you i've been burning my brain i just want to know how :((

So lets say we have r1 and r2. We want to know what r2-r1 is. So C1-C2=10, C1=2πr1 and C2=2πr2. Thus, 2πr2-2πr1=10, factor out to get 2π(r2-r1)=10, divide by 2π to get r2-r1=10/(2π). Then put this in calculator and round.

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.

Can you find a midpoint of three or even more given points? Or can there only be a midpoint for two given points?

You can have a "midpoint" of more than two points, but it may be called something else. For example, if you have a triangle, the incenter is equal distant from all three points, and you can find it by bisecting all the angles. This means there is not a nice formula like the midpoint formula of a line segment. I think there are limitations on 4 quadrilaterals, some can have a center point between the four points and some do not.

Main content

High school geometry

Course: High school geometry > Unit 6

Lesson 1: Distance and midpoints

Midpoint formula

CCSS.Math:

HSG.GPE.B.6

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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(34 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
  (12 votes)
Jade Slowik
Posted 6 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
(15 votes)
Answer
- John Williamson
  Posted 6 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 ...”
  (28 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)
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.
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(2 votes)
Answer
- Kendra Wilson
  Posted 6 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)
chloe johnson
Posted 2 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
- thebeaubennetts
  Posted 21 days ago. Direct link to thebeaubennetts's post “I do not think that there...”
  I do not think that there is an article or lesson about this but this is fairly simple. If given the one endpoint and a midpoint (as long as you now which one is which) all you have to do is find the change in x and the change in y of this and reflect it across the midpoint. Simply, all you have to do is reflect one endpoint across the midpoint and you will find the other endpoint. Hope this helps!
  Button navigates to signup page
  (1 vote)
wonderwoman
Posted 5 years ago. Direct link to wonderwoman's post “Hi, if you are given one ...”
Hi, if you are given one point and the midpoint, how do you find the other point? Is there a formula? I didn't find a video on it, only on finding the midpoint when given two points.
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(4 votes)
Answer
- Jerry Nilsson
  Posted 5 years ago. Direct link to Jerry Nilsson's post “We have a point 𝑃(𝑥₀, �...”
  We have a point 𝑃(𝑥₀, 𝑦₀) and a point 𝑀(𝑥₁, 𝑦₁), and we want to find the point 𝑄(𝑥₂, 𝑦₂) such that 𝑀 is the midpoint of segment 𝑃𝑄.
  
  If we view 𝑀 as the image of 𝑃 under translation 𝑇, we get
  𝑇 = ⟨𝑥₁ − 𝑥₀, 𝑦₁ − 𝑦₀⟩
  
  By applying the same translation to 𝑀, we get
  𝑄 = (𝑥₁ + (𝑥₁ − 𝑥₀), 𝑦₁ + (𝑦₁ − 𝑦₀)) = (2𝑥₁ − 𝑥₀, 2𝑦₁ − 𝑦₀)
  
  Example:
  𝑃 = (8, −10), 𝑀 = (−7, 3) ⇒
  ⇒ 𝑄 = (2・(−7) − 8, 2・3 − (−10)) = (−22, 16)
  Comment on Jerry Nilsson's post “We have a point 𝑃(𝑥₀, �...”
  (1 vote)
aliyahh.lequido
Posted 2 years ago. Direct link to aliyahh.lequido's post “The circumferences of two...”
The circumferences of two concentric circles differ by 10 inches. Compute the width of the ring between the two circles. Round off your answer to nearest hundredths place.
send help thank you i've been burning my brain i just want to know how :((
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “So lets say we have r1 an...”
  So lets say we have r1 and r2. We want to know what r2-r1 is. So C1-C2=10, C1=2πr1 and C2=2πr2.
  Thus, 2πr2-2πr1=10, factor out to get 2π(r2-r1)=10, divide by 2π to get r2-r1=10/(2π). Then put this in calculator and round.
  Button navigates to signup page
  (2 votes)
isaacong24
Posted 2 years ago. Direct link to isaacong24's post “Can you find a midpoint o...”
Can you find a midpoint of three or even more given points? Or can there only be a midpoint for two given points?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- David Severin
  Posted 2 years ago. Direct link to David Severin's post “You can have a "midpoint"...”
  You can have a "midpoint" of more than two points, but it may be called something else. For example, if you have a triangle, the incenter is equal distant from all three points, and you can find it by bisecting all the angles. This means there is not a nice formula like the midpoint formula of a line segment. I think there are limitations on 4 quadrilaterals, some can have a center point between the four points and some do not.
  Comment on David Severin's post “You can have a "midpoint"...”
  (3 votes)