Midpoint formula | Analytic geometry (article) | Khan Academy (2024)

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

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  • Alexene Faith S. Tomate

    8 years agoPosted 8 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?

    (38 votes)

    • Stephen

      4 years agoPosted 4 years ago. Direct link to Stephen's post “I believe you would simpl...”

      Midpoint formula | Analytic geometry (article) | Khan Academy (4)

      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.

      (22 votes)

  • Jade Slowik

    8 years agoPosted 8 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?

    (15 votes)

  • Humble Child Pööťý

    7 years agoPosted 7 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

    (5 votes)

    • David Severin

      7 years agoPosted 7 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.

      (9 votes)

  • Jonathan Huang

    8 years agoPosted 8 years ago. Direct link to Jonathan Huang's post “Why do we add instead of ...”

    Why do we add instead of subtract the numbers

    (5 votes)

    • Kim Seidel

      8 years agoPosted 8 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.

      (8 votes)

  • 8 years agoPosted 8 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?

    (4 votes)

  • baskarsandra

    8 years agoPosted 8 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.

    (1 vote)

    • Kendra Wilson

      7 years agoPosted 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.

      (9 votes)

  • XxGl1tchxX

    10 months agoPosted 10 months 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?

    (5 votes)

    • Derrick

      10 months agoPosted 10 months 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)

      (3 votes)

  • 26jamiras614

    a year agoPosted a year ago. Direct link to 26jamiras614's post “I am so confused but okay”

    I am so confused but okay

    (4 votes)

    • Kim Seidel

      a year agoPosted a year 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).

      (3 votes)

  • mrsdanielgray

    9 months agoPosted 9 months ago. Direct link to mrsdanielgray's post “Quite simple to me now.”

    Quite simple to me now.

    (4 votes)

  • chloe johnson

    a year agoPosted a year 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"

    (4 votes)

    • Aristotle

      a year agoPosted a year 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!

      (1 vote)

Midpoint formula | Analytic geometry (article) | Khan Academy (2024)

FAQs

What is the answer to the midpoint formula? ›

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.

How do you find the midpoint in geometry? ›

Explanation: You can find the midpoint of each coordinate by averaging them. In other words, add the two x coordinates together and divide by 2 and add the two y coordinates together and divide by 2.

What is the midpoint theorem in geometry? ›

The midpoint theorem states that “The line segment in a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

What is the midpoint method formula? ›

Midpoint Method vs Point Elasticity: Midpoint Method Formula

This average is calculated in the ( Q 2 + Q 1 ) / 2 and the ( P 2 + P 1 ) / 2 portions of the elasticity formula. This is where the midpoint method gets its name. The average is the midpoint between the old value and the new value.

How to teach midpoint formula? ›

The formula for finding the midpoint is M = ((x1 + x2)/2, (y1 + y2)/2), where M is the midpoint, x1 is the x-coordinate of point #1, x2 is the x-coordinate of point #2, y1 is the y-coordinate of point #1, and y2 is the y-coordinate of point #2. It does not matter which point is point #1 vs. point #2.

What is the rule of midpoint formula? ›

The midpoint can be found with the formula ((x1 + x2)/2, (y1 + y2)/2). Here (x1, y1), and (x2, y2) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.

What is the midpoint rule simplified? ›

The midpoint of a rectangle can be calculated by adding together the x-value of the rectangle's left limit with the x-value of the rectangle's right limit and dividing the sum by two.

What is the formula for the midpoint in 3d geometry? ›

Overview: A midpoint is the exact center point between two defined points. To find this center point, midpoint formula is applied. In 3-dimensional space, the midpoint between (x1, y1, z1) and (x2, y2, z1) is (x1+x2 )/2,(y1+y2 )/2,(z1+z2 )/2.

What is the midpoint formula used? ›

The midpoint of a line segment is the point at the exact middle of the line segment. The midpoint splits the line segment into two parts of the exact same length. The midpoint formula is ( x 1 + x 2 2 , y 1 + y 2 2 ) , where ( x 1 , y 1 ) and ( x 2 , y 2 ) are the endpoints of the line segment.

What is the formula for the midpoint in math is fun? ›

To calculate it: Add both "x" coordinates, divide by 2. Add both "y" coordinates, divide by 2.

What is the formula for the midpoint section? ›

Important Notes on Section Formula:

Section formula for external division is: P(x, y) = (mx2−nx1m−n,my2−ny1m−n) ( m x 2 − n x 1 m − n , m y 2 − n y 1 m − n ) Midpoint formula is: M(x, y) = (x2+x12,y2+y12) ( x 2 + x 1 2 , y 2 + y 1 2 )

What is an example of a midpoint? ›

For example, if we graph the two given points (2,2) and (8,6) on a coordinate plane, the midpoint is exactly halfway between the two, and lies at. ( 5 , 4 ) .

What is the midpoint formula form? ›

How do you Calculate Midpoint? The midpoint can be found with the formula ((x1 + x2)/2, (y1 + y2)/2). Here (x1, y1), and (x2, y2) are the coordinates of two points, and the midpoint is a point lying equidistant and between these two points.

What is the formula for the midpoint center? ›

The midpoint formula consists of two parts, one for the x-coordinate and another for the y-coordinate. For the x-coordinate, we add the x-values of both points (x+x) and divide the sum by 2. Similarly, for the y-coordinate, we add the y-values (y+y) and divide by 2.

How do you solve the midpoint rule? ›

The midpoint of a rectangle can be calculated by adding together the x-value of the rectangle's left limit with the x-value of the rectangle's right limit and dividing the sum by two.

What is the midpoint formula of section formula? ›

Section Formulae at a Glance
For Internal DivisionP={[(mx2+nx1)/(m+n)],[(my2+ny1)/(m+n)]}
For External DivisionP={[(mx2-nx1)/(m-n)],[(my2-ny1)/(m-n)]}
Midpoint FormulaP={(x1+x2)/2,(y1+y2)/2}

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