How does one derive the Midpoint Formula?

1 Answer
Daniel L.
Nov 23, 2015

It can be prooven using vectors. See explanation.

Explanation:

Let there be 2 points: A=(x_A;y_A) and B=(x_B,y_B). We are looking for a point M for which vectors vec(AM) and vec(MB) are equal. Using the equality of vectors we have:

[x_M-x_A;y_M-y_A]=[x_B-x_M;y_B-y_M].

Now we can calculate both coordinates separately:

x_M-x_A=x_B-x_M

x_M+x_M=x_B+x_A

2x_M=x_A+x_B

x_M=(x_A+x_B)/2

For y coordinate we have similar equation:

y_M-y_A=y_B-y_M

y_M+y_M=y_B+y_A

2y_M=y_A+y_B

y_M=(y_A+y_B)/2

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