Midpoint Formula

Key Questions

What is the Midpoint Formula?

Answer:

The coordinate of Midpoint $: (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $:((x_1+x_2)/2, (y_1+y_2)/2)$

Explanation:

Midpoint Formula :

$If A (x_{1}, y_{1}) and B (x_{2}, y_{2}) are the two point on the line ,$ $"If "A(x_1,y_1) and B(x_2,y_2) " are the two point on the line ,"$

$then midpoint M of the line segment ¯ ¯¯¯¯ ¯ A B is :$ $"then midpoint M of the line segment " bar(AB) " is :"$

$M (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ $M((x_1+x_2)/2, (y_1+y_2)/2)$

Please see the image.

maganbhai P. · 2 · Jul 24 2018
How do you apply the midpoint formula when the coordinates are fractions?

Answer:

You find the midpoint in exactly the same way with integers and fractions.

Explanation:

You find the midpoint in exactly the same way with integers and fractions, no matter whether they are common fractions, improper fractions or decimal fractions.

Add the two $x$ $x$ - values together and divide by $2$ $2$

Add the two $y$ $y$ -values together and divide by $2$ $2$

This will give a point, $M (x, y)$ $M(x,y)$

EZ as pi · 1 · Mar 4 2018
How do use midpoint formula to find an endpoint?

If you know one endpoint $(x_{1}, y_{1})$ $(x_1,y_1)$ and the midpoint $(a, b)$ $(a,b)$ , but you do not know the other endpoint $(x_{2}, y_{2})$ $(x_2,y_2)$ , then by rewriting the midpoint formula:

${(a={x_1+x_2}/2 Rightarrow 2a=x_1+x_2 Rightarrow x_2=2a-x_1),(b={y_1+y_2}/2 Rightarrow 2b=y_1+y_2 Rightarrowy_2=2b-y_1):}$

So, the unknown endpoint can be found by

$(x_2,y_2)=(2a-x_1,2b-y_1)$

I hope that this was helpful.

Wataru · 4 · Oct 29 2014
How does the midpoint formula involve finding averages?

The midpoint $M$ of the points $(x_1,y_1)$ and $(x_2,y_2)$ is found by

$M=({x_1+x_2}/2,{y_1+y_2}/2)$ .

As you can see above, the each coordinate of $M$ is the average of the corresponding coordinates of the endpoints.

I hope that this was helpful.

Wataru · 2 · Nov 1 2014