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.

      (23 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

      8 years agoPosted 8 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

    10 months agoPosted 10 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

Midpoint formula | Analytic geometry (article) | Khan Academy? ›

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.

How to calculate midpoint in geometry? ›

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.

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 correct midpoint formula? ›

The midpoint formula in coordinate geometry is defined as the formula to find the center point of a straight line, using the coordinates of its endpoints. It says the midpoint of a line segment with coordinates (x1 y1) and (x2, y2) is given by the formula ((x1 + x2)/2, (y1 + y2)/2).

How do you memorize the midpoint formula? ›

This looks complicated when written algebraically, but you're basically calculating the (mean) average of both the x values and the y values. Add the two x coordinates and divide by 2 to find the x coordinate of the midpoint, and add the two y coordinates and divide by 2 to find the y coordinate of the midpoint.

Where is the midpoint formula? ›

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 midpoint in geometry notes? ›

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).

What is midpoint in geometric terms? ›

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

What is the midpoint postulate in geometry? ›

Midpoint Formula: The midpoint of a segment is the point halfway across the segment. The midpoint of a segment in the x-y coordinate plane is found by averaging the two x-values and averaging the two y-values. The midpoint of a segment with endpoints (X1 , Y1 ) and ( X2 , Y2 ) in the x-y coordinate plane is…

What is the midpoint rule theorem? ›

The midpoint rule for estimating a definite integral uses a Riemann sum with subintervals of equal width and the midpoints, mi, of each subinterval in place of x∗i. Formally, we state a theorem regarding the convergence of the midpoint rule as follows. Mn=n∑i=1f(mi)Δx.

What is the formula for midpoint in coordinate geometry calculator? ›

You can find the midpoint of a line segment given 2 endpoints, (x1, y1) and (x2, y2). Add each x-coordinate and divide by 2 to find x of the midpoint. Add each y-coordinate and divide by 2 to find y of the midpoint.

What is the midpoint and distance in geometry? ›

The midpoint is the point that is an equal distance from both points and that lies on the line segment connecting the two points. You find the midpoint by adding the two x values together and dividing by 2, then adding the two y values together and dividing by 2.

Why use the midpoint formula? ›

The advantage of the midpoint method is that one obtains the same elasticity between two price points whether there is a price increase or decrease. This is because the formula uses the same base for both cases.

What is the midpoint method simplified? ›

The midpoint method uses the average or the midpoint between two data points to calculate the percent change in the price of a good and its percent change in quantity supplied or demanded. Those two values are then used to calculate the elasticity of supply and demand.

How to derive the midpoint formula? ›

The midpoint M is then defined by M = ((x + X)/2,(y + Y)/2). To show that M is really the midpoint of the line segment PQ, we need to show that the distance between M and Q is the same as the distance between M and P and that this distance is half the distance from P to Q.

What is the formula for the midpoint section? ›

Special Case: Midpoint Formula

When the point P(x, y) divides the line segment into two halves, we may say that P(x, y) is the midpoint of the line segment. By the use of section and midpoint formula: m : n = 1 : 1, since the line is divided into equal parts, we have.

How do you find the midpoint method? ›

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.

What is the formula for the midpoint of two points? ›

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.

How to calculate the midpoint between two numbers? ›

Midpoint is the point which is exactly in the middle of the two numbers. We can find the midpoint of the two given numbers by adding both the numbers and then dividing it by the number two. It is the average of the two numbers.

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